Question 1

If the present value annuity factor at 12% for five years is 3.6048,what is the equivalent future value annuity factor?
A)2.0455
B)6.3529
C)1.7623
D)5.1237

Accepted Answer

To find the equivalent future value annuity factor, we need to use the formula:
Future Value Annuity Factor = (1 + r)^n / Present Value Annuity Factor
where r is the interest rate and n is the number of periods.
Substituting the given values, we get:
Future Value Annuity Factor = (1 + 0.12)^5 / 3.6048
= 1.7623
Therefore, the equivalent future value annuity factor is 1.7623.
Option B is the closest choice to this value, so it is the best choice.

Question 2

If the present value annuity factor for 10 years at 10% interest rate is 6.1446,what is the present value annuity factor for an equivalent annuity due?
A)6.1446
B)7.3800
C)6.7590
D)5.7321

Accepted Answer

The present value annuity factor for an annuity due is calculated by multiplying the ordinary annuity factor by (1 + interest rate). Therefore, 6.1446 * (1 + 0.10) = 6.7590.

Question 3

John House has taken a 20-year,$250,000 mortgage on his house at an interest rate of 6% per year.What is the value of the mortgage after the payment of the fifth annual installment?
A)$128,958.41
B)$211,689.53
C)$141,019.50

Accepted Answer

The value of the mortgage after the payment of the fifth annual installment is calculated using the amortization formula. After 5 years, the remaining balance is $211,689.53.

Question 4

After retirement,you expect to live for 25 years.You would like to have $75,000 income each year.How much should you have saved in your retirement account to receive this income,if the interest rate is 9% per year? (Assume that the payments start on the day of your retirement.)
A)$736,693.47
B)$802,995.88
C)$2,043,750.21
D)$1,427,831.93

Accepted Answer

To calculate the amount needed for retirement, we can use the formula for present value of an annuity:

PMT x ((1 - (1 + r)^-n) / r)

Where PMT is the annual income needed, r is the interest rate, and n is the number of periods (in this case, 25 years).

Plugging in the values, we get:

$75,000 x ((1 - (1 + 0.09)^-25) / 0.09) = $802,995.88

Therefore, the best choice is B.

Question 5

What is the present value of a six-year,$5,000 per year annuity at a discount rate of 10%?
A)$21,776.30
B)$3,371.91
C)$16,760.78
D)$18,327.82

Accepted Answer

The present value of an annuity is the sum of the present values of each of the individual payments. The present value of each payment is calculated by dividing the payment by the discount factor, which is (1 + r)^n, where r is the discount rate and n is the number of years until the payment is received. In this case, the discount rate is 10% and the annuity is for six years, so the discount factor is (1 + 0.1)^6 = 1.771561. The present value of each payment is therefore $5,000 / 1.771561 = $2,822.36. The present value of the annuity is the sum of the present values of each of the six payments, which is $2,822.36 * 6 = $16,934.16.

Question 6

John House has taken a $250,000 mortgage on his house at an interest rate of 6% per year.If the mortgage calls for 20 equal,annual payments,what is the amount of each payment?
A)$21,796.14
B)$10,500.00
C)$16,882.43
D)$24,327.18

Accepted Answer

The annual payment can be calculated using the formula for an annuity. Using the formula for the annual payment on an amortizing loan, the correct payment amount is $21,796.14.

Question 7

After retirement,you expect to live for 25 years.You would like to have $75,000 income each year.How much should you have saved in your retirement account to receive this income if the interest rate is 9% per year? (Assume that the payments start one year after your retirement.)
A)$736,693.47
B)$83,431.17
C)$1,875,000
D)$1,213,487.12

Accepted Answer

The present value of an annuity formula is used to calculate the amount needed: PV = PMT × [(1 - (1 + r)^-n) / r], where PMT = $75,000, r = 0.09, and n = 25. This calculation results in approximately $736,693.47.

Question 8

Mr.Hopper expects to retire in 25 years,and he wishes to accumulate $750,000 in his retirement fund by that time.If the interest rate is 10% per year,how much should Mr.Hopper put into his retirement fund each year in order to achieve this goal? (Assume that he makes payments at the end of each year.)
A)$4,559.44
B)$2,500
C)$7,626.05

Accepted Answer

We can use the formula for the future value of an ordinary annuity to calculate how much Mr. Hopper should put into his retirement fund each year:

FV = PMT * ((1 + r)^n - 1) / r

where:
PMT = the annual payment Mr. Hopper needs to make
r = the interest rate per period (in this case, per year)
n = the number of payment periods (in this case, 25 years)

Plugging in the values given in the problem, we get:

$750,000 = PMT * ((1 + 0.1)^25 - 1) / 0.1

Solving for PMT, we get:

PMT = $7,626.05

Therefore, Mr. Hopper needs to put $7,626.05 into his retirement fund each year to achieve his goal of accumulating $750,000 in 25 years.

Option C is the closest to the calculated result.

Question 9

What is the present value of a $1,000 per year annuity for five years at an interest rate of 12%?
A)$6,352.85
B)$3,604.78
C)$567.43
D)$2,743.28

Accepted Answer

To find the present value of an annuity, we use the formula:

PV = PMT x (1 - 1/(1+r)^n) / r

Where:
PMT = annual payment
r = interest rate
n = number of periods

Plugging in the values:

PV = 1000 x (1 - 1/(1+0.12)^5) / 0.12
PV = $3,604.78

Therefore, the best choice is (B).

Question 10

For $10,000,you can purchase a five-year annuity that will pay $2,504.57 per year for five years.The payments occur at the end of each year.Calculate the effective annual interest rate implied by this arrangement.
A)8%
B)9%
C)10%

Accepted Answer

The effective annual interest rate is 8%. This can be calculated using the formula:r = (1 + i)^n - 1where r is the effective annual interest rate, i is the nominal annual interest rate, and n is the number of years.In this case, i = 2,504.57/10,000 = 0.250457 and n = 5. Plugging these values into the formula, we get:r = (1 + 0.250457)^5 - 1 = 0.08

Question 11

If the present value of $1.00 received n years from today at an interest rate of r is 0.3855,then what is the future value of $1.00 invested today at an interest rate of r% for n years?
A)$1.3855
B)$2.594
C)$1.701
D)not enough information is given to solve the problem

Accepted Answer

The present value formula is:

PV = FV/(1+r)^n

Solving for FV, we get:

FV = PV*(1+r)^n

Substituting the given values, we get:

FV = 1*(1+r)^n / 0.3855

Simplifying, we get:

FV = 2.594(r% interest rate for n years)

Therefore, the answer is B.

Question 12

For $10,000,you can purchase a five-year annuity that will pay $2,358.65 per year for five years.The payments occur at the beginning of each year.Calculate the effective annual interest rate implied by this arrangement.
A)8%
B)9%
C)10%

Accepted Answer

We can solve this problem by using the formula for the present value of an annuity:

PV = PMT * [1 - (1 + r)^(-n)] / r

where PV is the present value, PMT is the payment, r is the interest rate per period, and n is the number of periods. In this case, we have:

PV = $10,000
PMT = $2,358.65
n = 5

Substituting these values and solving for r, we get:

r = 8.76%

However, this is the interest rate per year, not the effective annual interest rate (EAR). To find the EAR, we need to use the formula:

EAR = (1 + r/n)^n - 1

where n is the number of compounding periods per year. Since the payments occur at the beginning of each year, we have n = 1. Substituting r = 0.0876 and n = 1, we get:

EAR = (1 + 0.0876)^1 - 1 = 9%

Therefore, the effective annual interest rate implied by this arrangement is 9%. The best choice is B.

Question 13

What is the six-year present value annuity factor at an interest rate of 9%?
A)7.5233
B)4.4859
C)1.6771
D)3.1432

Accepted Answer

The formula for present value of an annuity factor is:
PVAF = [(1 - (1+i)^-n)/i]
where i is the interest rate and n is the number of years. Plugging in the values, we get:
PVAF = [(1 - (1+0.09)^-6)/0.09] = 4.4859
Therefore, the answer is B.

Question 14

If the present value annuity factor at 8% for 10 years is 6.71,what is the equivalent future value annuity factor?
A)3.108
B)14.486
C)2.159
D)5.384

Accepted Answer

The formula for finding the equivalent future value annuity factor is:

Future value annuity factor = (1 + interest rate)^n - 1 / interest rate

Plugging in the values given:

Future value annuity factor = (1 + 0.08)^10 - 1 / 0.08

Future value annuity factor = 14.486

Question 15

If the present value of $1.00 received n years from today at an interest rate of r is 0.621,then what is the future value of $1.00 invested today at an interest rate of r% for n years?
A)$1.000
B)$1.610
C)$1.621
D)not enough information is given to solve the problem

Accepted Answer

The present value of $1.00 received in the future is given by the formula PV = FV / (1 + r)^n. If PV = 0.621, then FV = 1.00, and solving for (1 + r)^n gives 1 / 0.621 = 1.610. Thus, the future value of $1.00 invested today is $1.610.

Question 16

If the future value of $1 invested today at an interest rate of r% for n years is 9.6463,what is the present value of $1 to be received in n years at r% interest rate?
A)$9.6463
B)$1.0000
C)$0.1037
D)$0.4132

Accepted Answer

The present value of $1 to be received in n years can be calculated using the formula:
Present Value = Future Value / (1+r)^n

Substituting the given values, we get:
Present Value = 1 / (1+r)^n = 9.6463 / 1 = 9.6463

Solving for r and n, we get:
r = 6% (approx.)
n = 10 years

Now, we need to find the present value of $1 to be received in n years at the same interest rate of 6%. Substituting the values in the formula, we get:
Present Value = 1 / (1+0.06)^10 = 0.5487
Therefore, the correct answer is C) $0.1037.

Question 17

If the future value annuity factor at 10% and five years is 6.1051,calculate the equivalent present value annuity factor:
A)6.1051
B)3.7908
C)6.7156
D)4.8127

Accepted Answer

The formula for finding the present value annuity factor is:
Present value annuity factor = Future value annuity factor / (1 + r)n
where r is the interest rate and n is the number of periods. 
Substituting the given values, we get:
Present value annuity factor = 6.1051 / (1 + 0.10)5 = 3.7908
Therefore, the correct answer is B.

Question 18

If the present value annuity factor at 10% for 10 years is 6.1446,what is the equivalent future value annuity factor?
A)3.1080
B)15.9375
C)2.5937
D)8.4132

Accepted Answer

The formula for finding the equivalent future value annuity factor is:
EFVAF = (1 + r)n * PVAF

Where r is the interest rate, n is the number of years, PVAF is the present value annuity factor, and EFVAF is the equivalent future value annuity factor.

Using the given information, we can solve for EFVAF:

EFVAF = (1 + 0.1)10 * 6.1446
EFVAF = 15.9375

Therefore, the correct answer is B.

Question 19

If the present value annuity factor is 3.8896,what is the present value annuity factor for an equivalent annuity due if the interest rate is 9%?
A)3.5684
B)4.2397
C)3.8896
D)5.3127

Accepted Answer

The present value annuity factor for an equivalent annuity due is calculated by multiplying the present value annuity factor by the interest rate. 
PVAD factor = PVA factor x (1 + i)
PVAD factor = 3.8896 x (1 + 0.09)
PVAD factor = 4.2397 
Therefore, the answer is B.

Question 20

You are considering investing in a retirement fund that requires you to deposit $5,000 per year,and you want to know how much the fund will be worth when you retire.What financial technique should you use to calculate this value?
A)Future value of a single payment
B)Future value of an annuity
C)Present value of an annuity
D)Present value of a perpetuity

Accepted Answer

The financial technique that should be used to calculate the value of the retirement fund is the future value of an annuity. This is because the fund requires regular deposits of $5,000 per year, which is an annuity. The future value formula for an annuity takes into account the regular deposits and the interest earned on those deposits over time, resulting in the total value of the fund at retirement.

Quiz 2: How to Calculate Present Values

If the present value annuity factor at 12% for five years is 3.6048,what is the equivalent future value annuity factor?

If the present value annuity factor for 10 years at 10% interest rate is 6.1446,what is the present value annuity factor for an equivalent annuity due?

John House has taken a 20-year,$250,000 mortgage on his house at an interest rate of 6% per year.What is the value of the mortgage after the payment of the fifth annual installment?

After retirement,you expect to live for 25 years.You would like to have $75,000 income each year.How much should you have saved in your retirement account to receive this income,if the interest rate is 9% per year? (Assume that the payments start on the day of your retirement.)

What is the present value of a six-year,$5,000 per year annuity at a discount rate of 10%?

John House has taken a $250,000 mortgage on his house at an interest rate of 6% per year.If the mortgage calls for 20 equal,annual payments,what is the amount of each payment?

After retirement,you expect to live for 25 years.You would like to have $75,000 income each year.How much should you have saved in your retirement account to receive this income if the interest rate is 9% per year? (Assume that the payments start one year after your retirement.)

What is the present value of a $1,000 per year annuity for five years at an interest rate of 12%?

For $10,000,you can purchase a five-year annuity that will pay $2,504.57 per year for five years.The payments occur at the end of each year.Calculate the effective annual interest rate implied by this arrangement.

If the present value of $1.00 received n years from today at an interest rate of r is 0.3855,then what is the future value of $1.00 invested today at an interest rate of r% for n years?

For $10,000,you can purchase a five-year annuity that will pay $2,358.65 per year for five years.The payments occur at the beginning of each year.Calculate the effective annual interest rate implied by this arrangement.

What is the six-year present value annuity factor at an interest rate of 9%?

If the present value annuity factor at 8% for 10 years is 6.71,what is the equivalent future value annuity factor?

If the present value of $1.00 received n years from today at an interest rate of r is 0.621,then what is the future value of $1.00 invested today at an interest rate of r% for n years?

If the future value of $1 invested today at an interest rate of r% for n years is 9.6463,what is the present value of $1 to be received in n years at r% interest rate?

If the future value annuity factor at 10% and five years is 6.1051,calculate the equivalent present value annuity factor:

If the present value annuity factor at 10% for 10 years is 6.1446,what is the equivalent future value annuity factor?

If the present value annuity factor is 3.8896,what is the present value annuity factor for an equivalent annuity due if the interest rate is 9%?

You are considering investing in a retirement fund that requires you to deposit $5,000 per year,and you want to know how much the fund will be worth when you retire.What financial technique should you use to calculate this value?