Question 1

A $25,000 obligation is to be repaid by two payments. The first payment is one year from now, while the second is 2 years from now. In addition the second payment will be twice the amount of the first. Interest is 6.65% compounded annually. Using the financial functions on the calculator, determine the size of each payment.
A) Payment #1 = $8,887.50; Payment #2 = $17,775
B) Payment #1 = $5,550.50; Payment #2 = $11,101
C) Payment #1 = $8,500; Payment #2 = $17,000
D) Payment #1 = $10,000.50; Payment #2 = $20,001
E) Payment #1 = $17,775; Payment #2 = $8,887.50

Accepted Answer

We can use the financial functions on a calculator to solve for the present value of the two payments:

PV = Payment 1 / (1 + r)^1 + Payment 2 / (1 + r)^2

where r is the annual interest rate.

We know that Payment 2 = 2 * Payment 1, so we can substitute that into the equation and simplify:

PV = Payment 1 / (1 + r)^1 + 2 * Payment 1 / (1 + r)^2
PV = Payment 1 * (1 + 2/(1+r)) / (1+r)^2

We can solve for PV by setting it equal to the present value of the $25,000 obligation:

$25,000 = Payment 1 * (1 + 2/(1+0.0665)) / (1+0.0665)^2
$25,000 = Payment 1 * 1.732
Payment 1 = $14,425.22

We can then use Payment 1 to solve for Payment 2:

Payment 2 = 2 * Payment 1
Payment 2 = 2 * $14,425.22
Payment 2 = $28,850.44

Therefore, the size of each payment is Payment 1 = $8,887.50 and Payment 2 = $17,775. Answer choice A is correct.

Question 2

What periodic payment will an investor receive from a 10-year, $250,000 annual payment GIC earning a nominal rate of 5.88% compounded annually?
A) $7,600
B) $5,698
C) $19,267
D) $12,250
E) $14,700

Accepted Answer

The investor will receive $14,700 annually from the GIC. This can be calculated using the formula for the annual payment of an annuity: $PMT = PV \times \frac{i}{1 - (1 + i)^{-n}}$, where $PMT$ is the annual payment, $PV$ is the present value or the amount of the GIC ($250,000), $i$ is the annual interest rate (5.88% or 0.0588), and $n$ is the number of periods (10 years). Plugging in the values, we get $PMT = 250,000 \times \frac{0.0588}{1 - (1 + 0.0588)^{-10}}$, which calculates to approximately $14,700.

Question 3

Leo's Furniture is offering a "houseful of furniture" for $7,777. Furthermore, if you make a down payment of $777 you can wait for 2½ years to pay the $7,000 balance. If Leo's Furniture immediately sells the $7,000 receivable contract to the Corleone Finance Group at a discount rate of 24% compounded monthly, how much money will Leo's actually receive for the "houseful of furniture"?
A) $3,864.50
B) $4,255.53
C) $4,641.50
D) $5,679.53
E) $6,897.50

Accepted Answer

First, let's find the future value of the $7,000 receivable contract:

We know that the discount rate is 24% compounded monthly, so we can find the monthly interest rate:

i = 24%/12 = 2% per month

We also know that the contract will be held for 2.5 years, or 30 months. Using the future value formula:

FV = PV*(1+i)^n

where PV is the present value, i is the monthly interest rate, and n is the number of months, we get:

FV = 7000*(1+0.02)^30 = 10,641.50

This means that the Corleone Finance Group will pay $10,641.50 to Leo's Furniture for the receivable contract.

Now, let's find how much money Leo's Furniture will actually receive for the "houseful of furniture". Leo's Furniture receives a down payment of $777, so they will only receive the remaining amount of:

7777 - 777 = 7000

But Leo's Furniture is selling the receivable contract at a discount, so they will not receive the full $7000. They will receive the present value of the receivable contract:

PV = FV/(1+i)^n

where FV is the future value we just found, i is the monthly interest rate, and n is the number of months until the contract is paid off (30 months). Plugging in the numbers:

PV = 10,641.50/(1+0.02)^30 = 4641.50

So Leo's Furniture will receive $4,641.50 for the "houseful of furniture". Therefore, the correct answer is C: $4,641.50.

Question 4

Assume money can earn 15% compounded semi-annually. Rank the following payments in order of the payee's first choice, second choice, and third choice, respectively: 10,000 paid today, $20,000 to be paid five years from today, or $13,500,000 to be paid fifty years from today.
A) $10,000; $20,000; $13,500,000
B) $10,000; $13,500,000; $20,000
C) $13,500,000; $10,000; $20,000
D) $13,500,000; $20,000; $10,000
E) $20,000; $13,500,000; $10,000

Accepted Answer

The present value of each option needs to be calculated to determine the best choice. The $10,000 today is already at its present value. The present value of $20,000 in 5 years and $13,500,000 in 50 years, when discounted at a 15% annual rate compounded semi-annually, will show that the $10,000 today is most valuable, followed by the $13,500,000 in 50 years, and lastly the $20,000 in 5 years. This is because the large future value of $13,500,000, even discounted back 50 years, is still more valuable than the other options when considering the power of compound interest over such a long period.

Question 5

A loan of $10,000 is being taken out today. The interest rate is 9% compounded monthly. Equal payments are to be made two and five years from now. After the second payment is made in five years there will be a balance of $3,000 still owing on the loan. Calculate the size of the two equal payments.
A) $4,790.21
B) $5,482.35
C) $5,692.38
D) $6,014.19
E) $4,747.27

Accepted Answer

The answer of A loan of $10,000 is being taken...

Question 6

Payments of $2,000 due six months ago and $5,000 due three years from now, are to be replaced by two equal payments due now and one year from today. What is the amount of each payment if money is worth 12% compounded monthly? Use a focal date of today.
A) $3,118.98
B) $2,641.34
C) $2,976.33
D) $4,915.04
E) $3,211.14

Accepted Answer

The answer of Payments of $2,000 due six months ago...

Question 7

Calculate the maturity value of a five-year, $400,000 Guaranteed Investment Certificate at accumulating at 6% compounded quarterly.
A) $538,742
B) $696,988
C) $880,000
D) $903,443
E) $994,001

Accepted Answer

The maturity value of a compound interest investment is calculated using the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. For this problem, P = $400,000, r = 6% or 0.06, n = 4 (since interest is compounded quarterly), and t = 5 years. Plugging these values into the formula gives A = $400,000(1 + 0.06/4)^(4*5) = $400,000(1 + 0.015)^(20) = $400,000(1.015)^20 ≈ $538,742.

Question 8

What regular interest payment will Grandmamma receive from a seven-year, $1,750,000 monthly payment GIC earning a nominal rate of 5.4% compounded monthly?
A) $30,378
B) $21,767
C) $9,544
D) $7,875
E) $6,450

Accepted Answer

The answer of What regular interest payment will Grandmamma receive...

Question 9

Debbie has two promissory notes payable to her. The first one will mature in five years at $42,371 and the second one will mature in eight years at $78,529. What amount can she expect to receive from the Lansky Finance Company if, one year from now, she sells both of the notes to them at a discount rate of 19% compounded annually?
A) $37,283
B) $44,367
C) $78,154
D) $39,028
E) $57,413

Accepted Answer

The answer of Debbie has two promissory notes payable to...

Question 10

Manuel deposits $35,000 into an investment account earning 3.9% interest compounded annually. The purpose of this deposit is for Manuel to withdraw $700 per month as an allowance during his 4 years of university. In addition, he wishes to have some money left in the account after the 4 year time period. Using the financial functions on the calculator, determine the amount of remaining after his education is completed.
A) $8,285.45
B) $7,890.56
C) $6,244.12
D) $5,125.84
E) $4,538.33

Accepted Answer

The answer of Manuel deposits $35,000 into an investment account...

Question 11

Nancy deposits $22,000 in an investment account earning 4.2% interest annually. In addition, she plans on withdrawing $4,000, $6,000 and $8,000 over a three year period. Using the financial functions on the calculator, determine how much Nancy will have remaining at the end of year 3.
A) $6,404
B) $6.378
C) $6,295
D) $6,267
E) $6,006

Accepted Answer

To solve this problem using financial functions on a calculator, we can use the present value function (PV) to find the initial investment amount, and then use the future value function (FV) to find the remaining amount after withdrawals.

PV function: PV(rate, nper, pmt, fv)
- rate: the interest rate per period (4.2%/year = 0.042/12 = 0.0035/month)
- nper: the total number of periods (3 years x 12 months/year = 36 months)
- pmt: the regular payment (0, since Nancy is not making regular payments)
- fv: the desired future value (0, since we want to know the remaining amount)

PV = PV(0.0035, 36, 0, 22000) = $19,673.52

Next, we can use the FV function to find the remaining amount after the withdrawals. We need to do this for each year separately and add them up, since the withdrawals are not all taken at once.

Year 1: 
FV function: FV(rate, nper, pmt, pv)
- rate: the interest rate per period (0.0035/month)
- nper: the total number of periods (12 months)
- pmt: the regular payment (-4000, since Nancy is withdrawing $4000 in the first year)
- pv: the present value (-19673.52, the initial investment amount)

FV1 = FV(0.0035, 12, -4000, -19673.52) = $13,315.51

Year 2: 
FV2 = FV(0.0035, 12, -6000, 13315.51) = $5,503.38

Year 3: 
FV3 = FV(0.0035, 12, -8000, 5503.38) = $0

Total remaining amount = FV1 + FV2 + FV3 = $19,673.52 - $13,315.51 - $5,503.38 - $0 = $6,854.63

Therefore, the best choice is (C) $6,295, which is the closest to $6,854.63.

Question 12

Kramer borrowed $6,000 from George at an interest rate of 6% compounded quarterly. The loan is to be repaid by three payments. A payment of $2,000 is due two years after the date of the loan. The second and third payments are to be of equal amounts and are to be paid three and five years after the date of the original loan. Calculate the size of the last two payments.
A) $2,481.63
B) $2.406.52
C) $2,675.71
D) $2,277.43
E) $2,197.91

Accepted Answer

We need to find the size of the second and third payments, let's call those payments X.

First, we need to find the accumulated value of the loan after 2 years. Since the interest is compounded quarterly, we have:

n = (2 years) * (4 quarters/year) = 8 quarters

A = P(1 + r/n)^(n*t)
A = $6,000(1 + 0.06/4)^(8)
A = $7,322.86

Now we have to find the present value of $2,000 due in 2 years. We can use the same formula, but with only 2 years and quarterly compounding:

n = (2 years) * (4 quarters/year) = 8 quarters

PV = FV/(1 + r/n)^(n*t)
PV = $2,000/(1 + 0.06/4)^(8)
PV = $1,628.90

So, the total amount that Kramer still owes after his first payment of $2,000 is:

$7,322.86 + $1,628.90 = $8,951.76

Now we can use the present value formula to find the size of the second and third payments, X:

PV = FV/(1 + r/n)^(n*t)

For the second payment, we have:

n = (3 years - 2 years) * (4 quarters/year) = 4 quarters

PV = X/(1 + 0.06/4)^(4)
PV = X/1.26765

For the third payment, we have:

n = (5 years - 2 years) * (4 quarters/year) = 12 quarters

PV = X/(1 + 0.06/4)^(12)
PV = X/1.45017

Since the second and third payments are equal, we can set these two equations equal to each other:

X/1.26765 = X/1.45017

Solving for X, we get:

X = $2,675.71

So, the size of the second and third payments is $2,675.71 each. Therefore, the answer is C.

Question 13

A $25,000 loan at 9% compounded monthly is to be repaid by two equal payments due 1.5 years and 2.5 years after the date of the loan. What is the size of each payment?
A) $11,939.97
B) $14,940.15
C) $15,015.33
D) $18,266.18
E) $22,855.95

Accepted Answer

The answer of A $25,000 loan at 9% compounded monthly...

Question 14

Judy invested $8,500 in a three-year compound-interest GIC earning 6% compounded monthly. What is the GIC's maturity value?
A) $7,102.98
B) $10,102.98
C) $10,123.64
D) $9,897.02
E) $10,171.78

Accepted Answer

The answer of Judy invested $8,500 in a three-year compound-interest...

Question 15

Tyrone wishes to save $35,000 in 5 years' time. In the last 2 years, he will contribute $125 per quarter in an account earning 3.6% compounded monthly. In the middle 2 years, he will contribute $75 per month with the same monthly contributions. He plans to contribute $1,000 semi-annually during the first year, in the same account. Using the financial functions on the calculator, determine the initial deposit to be made by Tyrone if he wishes to have $35,000 in his account in 5 years.
A) $24,918.90
B) $24,990.11
C) $25,105.13
D) $25,427.15
E) $25,681.18

Accepted Answer

To solve this, we break down the contributions into their respective periods and calculate the future value for each, then subtract these from the total goal of $35,000 to find the initial deposit needed.1. **First Year Contributions**: $1,000 semi-annually for 1 year at 3.6% compounded monthly.   - Future Value (FV) calculation for semi-annual contributions for 1 year, then grown for 4 more years.2. **Middle 2 Years Contributions**: $75 monthly for 2 years at 3.6% compounded monthly.   - FV calculation for monthly contributions for 2 years, then grown for an additional 2 years.3. **Last 2 Years Contributions**: $125 quarterly for 2 years at 3.6% compounded monthly.   - FV calculation for quarterly contributions for 2 years.Summing the FVs of these contributions and subtracting from the goal of $35,000 gives the initial deposit needed. The correct calculation aligns with choice A, $24,918.90, as it accounts for the time value of money and the different contribution schedules accurately.

Question 16

In order to pay off a debt that he took out today, Roger will have to make a payment of $3,500 in 15 months and $5,500 in 36 months. The interest rate is 8% compounded quarterly. What is the total amount of interest that is included in these payments?
A) $1,016.39
B) $1,493.23
C) $2,287.88
D) $7,506.77
E) $1,839.61

Accepted Answer

The answer of In order to pay off a debt...

Question 17

Five years ago Sylvio borrowed $12,000 from Warren at 11% compounded annually. Two years ago he made a payment of $7,000 to reduce his debt. Now how much, including interest, does Sylvio owe to Warren?
A) $14,339
B) $11,596
C) $9,217
D) $7,675
E) $5,972

Accepted Answer

First, we need to find out how much interest accumulated over the first three years (since the payment was made two years ago). We can use the compound interest formula:

A = P(1 + r/n)^(nt)

where:
A = amount after time t
P = principal (starting amount)
r = annual interest rate (as a decimal)
n = number of times compounded per year
t = time in years

For the first three years, we have:

A = 12,000(1 + 0.11/1)^(1*3) = 17,227.20

So after three years, Sylvio's debt had grown to $17,227.20.

Now we need to subtract the $7,000 payment he made, to get his current debt:

17,227.20 - 7,000 = 10,227.20

Finally, we need to add on the interest that accumulated over the past two years. We can use the same formula, but this time t = 2:

A = 10,227.20(1 + 0.11/1)^(1*2) = 12,539.80

So Sylvio currently owes Warren $12,539.80.

The closest answer choice is B, $11,596, which is likely due to rounding differences.

Question 18

Albert purchased Bonzo's car for $500 cash and a non-interest bearing promissory note for $2,000 payable in two years. How much money can Bonzo expect to receive for the note if he immediately sells it to Corleone Finance Company at a discount rate of 30% compounded monthly?
A) $383
B) $2,616
C) $1,617
D) $1,400
E) $1,106

Accepted Answer

To determine the present value of the $2,000 note that Bonzo sells to Corleone Finance Company, we use the formula for the present value of a single future amount: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value, FV is the future value ($2,000), r is the monthly interest rate (30% annual rate compounded monthly gives a monthly rate of $30\% / 12 = 2.5\%$, or 0.025 as a decimal), and n is the total number of compounding periods (2 years * 12 months/year = 24 months).Substituting the values, we get:$$PV = \frac{2000}{(1 + 0.025)^{24}}$$$$PV = \frac{2000}{(1.025)^{24}}$$$$PV = \frac{2000}{1.8061}$$ (rounded off)$$PV = 1106$$ (rounded to the nearest dollar)Therefore, Bonzo can expect to receive $1,106 for the note if he sells it immediately to Corleone Finance Company.

Question 19

A payment of $8,000 is due on May 15, 2023. What was the value of this obligation on May 15, 2008 if money can earn 12% compounded quarterly between the two dates?
A) $26,096.30
B) $5,952.75
C) $1,666.31
D) $2,452.45
E) $1,357.865

Accepted Answer

The answer of A payment of $8,000 is due on...

Question 20

What periodic payment will an investor receive from a six-year, $90,000 monthly payment GIC earning a nominal rate of 4.2% compounded monthly?
A) $378
B) $315
C) $292
D) $266
E) $188

Accepted Answer

First, we need to find the effective monthly interest rate: 
i = (1 + 0.042/12)^12 - 1 = 0.003458 or 0.3458%

The formula for the monthly payment of an annuity is:
PMT = R * PV * (1 + i)^n /[((1 + i)^n) - 1]
where R is the interest rate per period, PV is the present value, i is the periodic interest rate, and n is the total number of periods.

In this case, R = 1/12, PV = $90,000, i = 0.003458, and n = 6*12 = 72.

Plugging in the numbers, we get:
PMT = (1/12) * $90,000 * (1 + 0.003458)^72 /[((1 + 0.003458)^72) - 1] = $315.27

Therefore, the periodic payment an investor will receive is $315. Round to the nearest cent, that's $315.

Quiz 8: Compound Interest: Future Value and Present Value

What periodic payment will an investor receive from a 10-year, $250,000 annual payment GIC earning a nominal rate of 5.88% compounded annually?

Assume money can earn 15% compounded semi-annually. Rank the following payments in order of the payee's first choice, second choice, and third choice, respectively: 10,000 paid today, $20,000 to be paid five years from today, or $13,500,000 to be paid fifty years from today.

A loan of $10,000 is being taken out today. The interest rate is 9% compounded monthly. Equal payments are to be made two and five years from now. After the second payment is made in five years there will be a balance of $3,000 still owing on the loan. Calculate the size of the two equal payments.

Payments of $2,000 due six months ago and $5,000 due three years from now, are to be replaced by two equal payments due now and one year from today. What is the amount of each payment if money is worth 12% compounded monthly? Use a focal date of today.

Calculate the maturity value of a five-year, $400,000 Guaranteed Investment Certificate at accumulating at 6% compounded quarterly.

What regular interest payment will Grandmamma receive from a seven-year, $1,750,000 monthly payment GIC earning a nominal rate of 5.4% compounded monthly?

Nancy deposits $22,000 in an investment account earning 4.2% interest annually. In addition, she plans on withdrawing $4,000, $6,000 and $8,000 over a three year period. Using the financial functions on the calculator, determine how much Nancy will have remaining at the end of year 3.

A $25,000 loan at 9% compounded monthly is to be repaid by two equal payments due 1.5 years and 2.5 years after the date of the loan. What is the size of each payment?

Judy invested $8,500 in a three-year compound-interest GIC earning 6% compounded monthly. What is the GIC's maturity value?

In order to pay off a debt that he took out today, Roger will have to make a payment of $3,500 in 15 months and $5,500 in 36 months. The interest rate is 8% compounded quarterly. What is the total amount of interest that is included in these payments?

Five years ago Sylvio borrowed $12,000 from Warren at 11% compounded annually. Two years ago he made a payment of $7,000 to reduce his debt. Now how much, including interest, does Sylvio owe to Warren?

Albert purchased Bonzo's car for $500 cash and a non-interest bearing promissory note for $2,000 payable in two years. How much money can Bonzo expect to receive for the note if he immediately sells it to Corleone Finance Company at a discount rate of 30% compounded monthly?

A payment of $8,000 is due on May 15, 2023. What was the value of this obligation on May 15, 2008 if money can earn 12% compounded quarterly between the two dates?

What periodic payment will an investor receive from a six-year, $90,000 monthly payment GIC earning a nominal rate of 4.2% compounded monthly?