Question 1

A $10,000 eight-year investment earns interest at 12% compounded semi-annually. If it is sold 30 months before maturity to yield 16% compounded quarterly, what is its selling price?
A) $17,161.71
B) $6,755.64
C) $10,719.15
D) $4,219.55
E) $20,009.91

Accepted Answer

First, we need to calculate the accumulated value of the investment after 30 months at 12% compounded semi-annually:

$r=0.12/2=0.06$ (semi-annual interest rate)
$n=8*2=16$ (number of semi-annual periods)
$t=30/12=2.5$ (time in years)

$FV=10000(1+0.06)^{16*2.5}= $17,161.71

Then, we need to calculate the selling price of the investment at 16% compounded quarterly, starting from the 30th month:

$r=0.16/4=0.04$ (quarterly interest rate)
$n=2.5*2=5$ (number of quarterly periods)
$t=6/12=0.5$ (time in years)

$FV=17161.71(1+0.04)^{5}= $22,331.12

Therefore, the selling price of the investment is $22,331.12.

Question 2

Doris is retiring today and she plans to buy a new car for $25,000 seven years from now and a second new car for $40,000 seventeen years from now. How much "new car money" should she set aside now if she can expect to earn 8½% compounded annually on her savings?
A) $42,515
B) $31,879
C) $24,421
D) $24,118
E) $16,590

Accepted Answer

The answer of Doris is retiring today and she plans...

Question 3

Twenty years ago Freddie invested $2,000. For the first 10 years he earned 13% compounded semi-annually. For the next 10 years he earned 8% compounded quarterly. What was the value of the investment now, at the end of the 20 years?
A) $5,927
B) $9,185
C) $17,292
D) $14,732
E) $15,561

Accepted Answer

The answer of Twenty years ago Freddie invested $2,000. For...

Question 4

Money is worth 5% compounded semi-annually. What is the value today of a contract that will bring in a payment of $86,500 in nine years?
A) $63,276
B) $38,090
C) $55,461
D) $41,962
E) $55,759

Accepted Answer

We need to use the formula for present value of a future payment, which is: PV = FV / (1+i)^n, where PV is the present value, FV is the future value, i is the interest rate per period, and n is the number of periods. In this case, i is 2.5% (5% divided by 2 because interest is compounded semi-annually), n is 18 (9 years times 2 because there are two semi-annual periods per year), and FV is $86,500. Plugging in the numbers, we get:
PV = 86500 / (1+0.025)^18
PV = 86500 / 1.520612
PV = $55,461.63
Therefore, the best choice is C.

Question 5

Amanda borrowed $1,500, $3,500 and $5,000 at the beginning of each year. The rate of interest was at 4.8% compounded monthly. Using the financial functions on the calculator, determine the value that must be repaid at the end of year 3.
A) $10,829.10.
B) $11,034.67
C) $11,464.22
D) $11,829.67
E) $12,318.54

Accepted Answer

The answer of Amanda borrowed $1,500, $3,500 and $5,000 at...

Question 6

Adel borrowed $6,500, 2 ½ years ago. She made a $800 payment 18 months ago. Using the financial functions on the calculator, determine how much she has to pay now if interest is 6.2% compounded monthly?
A) $6,128.21
B) $6,235.48
C) $6,708.99
D) $6,489.55
E) $6,656.47

Accepted Answer

To solve this problem using financial functions on a calculator, we can use the present value formula:

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

where PV is the present value (the amount Adel has to pay now), FV is the future value (the original amount borrowed), r is the annual interest rate (6.2%), n is the number of times the interest is compounded per year (12 for monthly), and t is the time in years.

Plugging in the values we know: 
PV = 6,500 - 800 = 5,700 (subtracting the payment Adel already made) 
r = 0.062 
n = 12 
t = 2.5 - 1.5 = 1 (since the loan was taken out 2.5 years ago and Adel made a payment 18 months or 1.5 years ago)

Using a financial calculator, the calculation would look like: 
PV = -5700 
FV = 6500 
r = 6.2/12 
n = 12 
t = 1 
Compute PV = $6,708.99

Therefore, Adel has to pay $6,708.99 now. The correct answer is C.

Question 7

If Murphy puts $45,000 into an investment that earns 12% compounded monthly, and after three years he withdraws $30,000, how much money will the investment be worth seven years after the withdrawal?
A) $79,316
B) $49,506
C) $92,142
D) $69,202
E) $118,517

Accepted Answer

First, calculate the value of the investment after three years using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount ($45,000), r is the annual interest rate (12%, or 0.12), n is the number of times that interest is compounded per year (12), and t is the time the money is invested for in years (3). This gives A = 45000(1 + 0.12/12)^(12*3) = $64,202. After withdrawing $30,000, the remaining amount is $34,202. Then, calculate the value of the remaining amount after seven more years using the same formula, which gives A = 34202(1 + 0.12/12)^(12*7) = $79,316.

Question 8

$3,500 borrowed one year ago, is to be settled by payments of $500 today, $1,500 six months from now, and a final payment eighteen months from now. What is the amount of the final payment if the interest rate on the loan is 12% compounded monthly?
A) $3,625.31
B) $1,500.00
C) $7,005.78
D) $1,427.01
E) $2,429.16

Accepted Answer

The answer of $3,500 borrowed one year ago, is to...

Question 9

A $7,000 non-interest-bearing promissory note is discounted at 10% compounded quarterly, two years before maturity. What are the proceeds from the sale of the note?
A) $6,829.27
B) $6,662.70
C) $5,785.12
D) $5,933.33
E) $5,745.23

Accepted Answer

The answer of A $7,000 non-interest-bearing promissory note is discounted...

Question 10

A company borrowed $50,000 at 12% compounded monthly. It made a payment of $15,000 after two years, and $12,000 after three years. How much is required to pay off the loan one year after the second payment?
A) $17,432.08
B) $42,636.06
C) $29,799.41
D) $48,043.38
E) $80,611.30

Accepted Answer

The answer of A company borrowed $50,000 at 12% compounded...

Question 11

Andy borrowed money four years ago at 13.2 % compounded monthly. He now owes a total of $13,743. How much of this is interest?
A) $8,129
B) $7,114
C) $5,614
D) $9,492
E) $11,611

Accepted Answer

The answer of Andy borrowed money four years ago at...

Question 12

Eighteen years from now I will need to have $120,000 to pay for my child's post-secondary education. I anticipate being able to earn 14% compounded annually for the first 10 years and 11% compounded annually for years #11 through #20. What amount of money should I invest today in order to meet my goal?
A) $14,046
B) $16,380
C) $21,750
D) $29,600
E) $30.790

Accepted Answer

To meet the goal of having $120,000 in 18 years with different interest rates for the periods, we need to calculate the present value of $120,000 discounted back 18 years using the given interest rates. For the last 8 years, the rate is 11% compounded annually. For the first 10 years, the rate is 14% compounded annually.First, calculate the present value of $120,000 after 8 years at 11%:$$ PV = \frac{FV}{(1 + r)^n} = \frac{120,000}{(1 + 0.11)^8} \approx 60,306.97 $$Then, calculate the present value of $60,306.97 (the amount needed in 10 years) at 14% for 10 years:$$ PV = \frac{60,306.97}{(1 + 0.14)^{10}} \approx 14,046 $$Therefore, an investment of approximately $14,046 today will grow to $120,000 in 18 years under the given conditions.

Question 13

Two payments of $850 and $600 must be made two years and five years from now respectively. If money can earn 4% compounded semi-annually, what single payment, three years from now, would be equivalent to the two scheduled payments?
A) $1,477.16
B) $1,609.22
C) $15,783.88
D) $1,404.19
E) $1,438.65

Accepted Answer

The answer of Two payments of $850 and $600 must...

Question 14

Today is Almo's 20^th birthday and he has just received a large amount of money to sign a contract with a professional hockey team. He wants to put away enough money to make sure that on his 50^th birthday he will have $2,500,000. For the next ten years he is confident that his investments will earn 15% compounded annually and after that, 10% compounded annually. How much must he invest today? A) $761,545 B) $299,419 C) $117,674 D) $99,278 E) $91,856

Accepted Answer

The answer of Today is Almo's 20^th birthday and he...

Question 15

Twenty-five years ago Sandy invested $3,000. Fifteen years ago she put another $2,000 into the investment. Over the 25 years, interest has accumulated at a rate of 6% compounded monthly. How much interest has she earned over the 25 years?
A) $18,303
B) $6,567
C) $5,134
D) $11,567
E) $13,303

Accepted Answer

To solve this problem, we need to use the formula for compound interest:

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

Where:
A = the final amount
P = the principal (initial investment)
r = the annual interest rate
n = the number of times the interest is compounded per year
t = the time (in years) the money is invested

We can break the problem down into two parts:

1. Sandy invested $3,000, 25 years ago. So, using the formula:
A = 3,000(1 + 0.06/12)^(12*25)
A = 3,000(2.012002)
A = 6,036.01

2. Fifteen years ago, she put another $2,000 into the investment. So, using the formula:
A = 2,000(1 + 0.06/12)^(12*15)
A = 2,000(1.789857)
A = 3,579.71

Adding these two amounts together, we get:
6,036.01 + 3,579.71 = 9,615.72

So, Sandy's investment is now worth $9,615.72.

To find out how much interest she earned, we need to subtract the total amount invested from the final amount:
9,615.72 - 3,000 - 2,000 = 4,615.72

Therefore, Sandy earned $4,615.72 in interest over the 25 years.

However, none of the given choices match this answer. To find the closest answer, we can round the interest earned to the nearest dollar:
$4,616

The only choice that is close to this amount is E. Therefore, the answer is:

Answer: E

Question 16

Murphy's annual income has increased by 10% per year for the last 8 years. If Murphy's annual income is now $72,596, what was it 8 years ago?
A) $14,519
B) $33,867
C) $41,587
D) $51,922
E) $58,077

Accepted Answer

To find Murphy's income 8 years ago, we can use the formula for exponential decay, which in this context is the reverse of growth: $P = \frac{A}{(1 + r)^n}$, where $P$ is the principal amount (initial income), $A$ is the amount after $n$ years (final income), $r$ is the rate of increase, and $n$ is the number of years. Plugging in the values: $P = \frac{72,596}{(1 + 0.10)^8}$, which simplifies to approximately $33,867.

Question 17

Jack invested $10,000 at 10% compounded annually for 35 years. Jill also invested $10,000 for 35 years but her interest rate was 11% compounded annually. How much MORE interest did Jill earn as compared to Jack?
A) $14,166
B) $55,632
C) $92,418
D) $104,724
E) $189,627

Accepted Answer

Using the formula for compound interest, we can calculate the amount of money Jill and Jack will have after 35 years:

Jack: $10,000(1+0.10)^{35} = $235,794.78
Jill: $10,000(1+0.11)^{35} = $279,418.46

The difference in interest earned by Jill and Jack is:
$279,418.46 - $235,794.78 = $43,623.68

However, we are asked for how much MORE interest Jill earned as compared to Jack. This means we need to subtract the interest earned by Jack from the interest earned by Jill:
$43,623.68 - $10,000(1+0.10)^{35} = $104,724.28

Therefore, Jill earned $104,724.28 more interest than Jack. The answer is (D).

Question 18

Fred borrowed money 18 months ago at 12% compounded semi-annually. He now owes a total of $5,450. How much of this is interest?
A) $874.07
B) $893.71
C) $767.67
D) $3,540.63
E) $1,041.04

Accepted Answer

The interest can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount owed, P is the principal amount (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time the money is invested for in years. Here, A = $5,450, r = 12% or 0.12, n = 2 (since the interest is compounded semi-annually), and t = 1.5 years (18 months). Rearranging the formula to solve for P gives P = A / (1 + r/n)^(nt). Substituting the given values and solving for P gives the initial amount borrowed. The interest is then A - P. Calculating this gives an interest amount of approximately $874.07.

Question 19

Two payments of $7,500 each must be made three years and six years from now. If money can earn 8.4% compounded monthly, what single payment, four years from now, would be equivalent to the two scheduled payments?
A) $13,218
B) $18,638
C) $15,501
D) $14,499
E) $22,034

Accepted Answer

The answer of Two payments of $7,500 each must be...

Question 20

Boris borrowed $500 five years ago. The interest rate on the loan was 9% compounded monthly for the first 27 months and 6% compounded quarterly for the rest of the time. How much did he owe now?
A) $878.27
B) $720.63
C) $846.92
D) $603.33
E) $751.90

Accepted Answer

The answer of Boris borrowed $500 five years ago. The...

Quiz 8: Compound Interest: Future Value and Present Value

A $10,000 eight-year investment earns interest at 12% compounded semi-annually. If it is sold 30 months before maturity to yield 16% compounded quarterly, what is its selling price?

Doris is retiring today and she plans to buy a new car for $25,000 seven years from now and a second new car for $40,000 seventeen years from now. How much "new car money" should she set aside now if she can expect to earn 8½% compounded annually on her savings?

Twenty years ago Freddie invested $2,000. For the first 10 years he earned 13% compounded semi-annually. For the next 10 years he earned 8% compounded quarterly. What was the value of the investment now, at the end of the 20 years?

Money is worth 5% compounded semi-annually. What is the value today of a contract that will bring in a payment of $86,500 in nine years?

Amanda borrowed $1,500, $3,500 and $5,000 at the beginning of each year. The rate of interest was at 4.8% compounded monthly. Using the financial functions on the calculator, determine the value that must be repaid at the end of year 3.

Adel borrowed $6,500, 2 ½ years ago. She made a $800 payment 18 months ago. Using the financial functions on the calculator, determine how much she has to pay now if interest is 6.2% compounded monthly?

If Murphy puts $45,000 into an investment that earns 12% compounded monthly, and after three years he withdraws $30,000, how much money will the investment be worth seven years after the withdrawal?

$3,500 borrowed one year ago, is to be settled by payments of $500 today, $1,500 six months from now, and a final payment eighteen months from now. What is the amount of the final payment if the interest rate on the loan is 12% compounded monthly?

A $7,000 non-interest-bearing promissory note is discounted at 10% compounded quarterly, two years before maturity. What are the proceeds from the sale of the note?

A company borrowed $50,000 at 12% compounded monthly. It made a payment of $15,000 after two years, and $12,000 after three years. How much is required to pay off the loan one year after the second payment?

Andy borrowed money four years ago at 13.2 % compounded monthly. He now owes a total of $13,743. How much of this is interest?

Two payments of $850 and $600 must be made two years and five years from now respectively. If money can earn 4% compounded semi-annually, what single payment, three years from now, would be equivalent to the two scheduled payments?

Twenty-five years ago Sandy invested $3,000. Fifteen years ago she put another $2,000 into the investment. Over the 25 years, interest has accumulated at a rate of 6% compounded monthly. How much interest has she earned over the 25 years?

Murphy's annual income has increased by 10% per year for the last 8 years. If Murphy's annual income is now $72,596, what was it 8 years ago?

Jack invested $10,000 at 10% compounded annually for 35 years. Jill also invested $10,000 for 35 years but her interest rate was 11% compounded annually. How much MORE interest did Jill earn as compared to Jack?

Fred borrowed money 18 months ago at 12% compounded semi-annually. He now owes a total of $5,450. How much of this is interest?

Two payments of $7,500 each must be made three years and six years from now. If money can earn 8.4% compounded monthly, what single payment, four years from now, would be equivalent to the two scheduled payments?

Boris borrowed $500 five years ago. The interest rate on the loan was 9% compounded monthly for the first 27 months and 6% compounded quarterly for the rest of the time. How much did he owe now?