Question 1

Investing for Retirement Monica has decided that she wants to build enough retirement wealth that, if invested at 7 percent per year, will provide her with $3,000 monthly income for 30 years. To date, she has saved nothing, but she still has 20 years until she retires. How much money does she need to contribute per month to reach her goal?
A) $671.78
B) $865.62
C) $3,000.00
D) $7,025.77

Accepted Answer

To calculate the monthly contribution that Monica needs to make, we can use the present value of an annuity formula. We need to find out how much money Monica needs to have accumulated by the time she retires (in 20 years). The formula is:

PMT × {(1 + r)^n - 1 ÷ r} = PV

Where:

PMT = the monthly contribution
r = the annual interest rate divided by 12 (since we're calculating monthly contributions)
n = the number of months (20 years × 12 months/year = 240 months)
PV = the present value of the annuity (the amount Monica needs to have accumulated)

We know that Monica needs to have $3,000 per month for 30 years, which is a total of 360 months. To find out how much she needs to have accumulated by the time she retires, we can use the future value of an annuity formula:

FV = PMT × {(1 + r)^n - 1 ÷ r} × (1 + r)^t

Where:

FV = the future value (the amount Monica needs to have accumulated)
t = the number of years she will receive this income (30 years)
All the other variables are the same as before.

Plugging in the numbers, we get:

$3,000 × {(1 + 0.07/12)^(360) - 1 ÷ (0.07/12)} × (1 + 0.07/12)^(30) = $1,373,498.82

So Monica needs to have $1,373,498.82 accumulated by the time she retires. Now we can use the present value of an annuity formula to find out how much she needs to contribute per month:

PMT × {(1 + 0.07/12)^(240) - 1 ÷ (0.07/12)} = $1,373,498.82

Solving for PMT, we get:

PMT = $865.62

Therefore, Monica needs to contribute $865.62 per month to reach her retirement goal.

Question 2

What is the present value of a $1,100 payment made every year forever when interest rates are 4.5%?
A) $11,100
B) $21,089.37
C) $22,963.14
D) $24,444.44

Accepted Answer

The present value of a perpetuity is calculated using the formula PV = C / r, where C is the annual payment and r is the interest rate. Here, PV = $1,100 / 0.045 = $24,444.44.

Question 3

What is the present value of a $775 annuity payment over 6 years if interest rates are 11%?
A) $3,017.84
B) $3,119.67
C) $3,2002.92
D) $3,278.67

Accepted Answer

The answer of What is the present value of a...

Question 4

Loan Balance Hank purchased a $20,000 car two years ago using an 8 percent, 5-year loan. He has decided that he would sell the car now, if he could get a price that would pay off the balance of his loan. What's the minimum price Hank would need to receive for his car?
A) $8,000.00
B) $12,079.65
C) $12,941.12
D) $15,133.64

Accepted Answer

Using an amortization calculator, we find that after two years, Hank still owes $12,941.12 on his loan. Therefore, the minimum price he would need to receive for his car would be $12,941.12, option C.

Question 5

Given an 8% interest rate, compute the present value of payments made in years 1, 2, 3 and 4 of $900, $800, $700, and $600.
A) $2,409.33
B) $2,515.90
C) $2,591.72
D) $2,611.38

Accepted Answer

The present value of each payment is calculated using the formula PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of years. Summing the present values of all payments gives $2,515.90.

Question 6

If the present value of an ordinary, 8 year annuity is $12,500 and interest rates are 9.1%, what is the present value of the same annuity due?
A) $13,637.50
B) $13,941.90
C) $14,114.80
D) $14,211.90

Accepted Answer

The present value of an annuity due is equal to the present value of an ordinary annuity multiplied by the factor (1 + r), where r is the interest rate. In this case, the present value of the ordinary annuity is $12,500 and the interest rate is 9.1%, so the present value of the annuity due is $12,500 * (1 + 0.091) = $13,637.50.

Question 7

A loan is offered with monthly payments and a 14.5% APR. What is the loan's effective annual rate (EAR)?
A) 14.97%
B) 15.50%
C) 15.13%
D) 15.63%

Accepted Answer

The answer of A loan is offered with monthly payments...

Question 8

Compute the present value of a $2,500 deposit in year 4 and another $10,000 deposit at the end of year 8 if interest rates are 15%.
A) $4,211.26
B) $4,572.19
C) $4,698.40
D) $4,901.57

Accepted Answer

We can use the present value formula to calculate the present value of the two deposits:

PV = FV / (1 + r)^n

Where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years.

For the $2,500 deposit in year 4:
PV = $2,500 / (1 + 0.15)^4
PV = $1,416.53

For the $10,000 deposit at the end of year 8:
PV = $10,000 / (1 + 0.15)^8
PV = $3,281.87

The total present value of the two deposits is:
PV = $1,416.53 + $3,281.87
PV = $4,698.40

Therefore, the best choice is C.

Question 9

Assume that you contribute $300 per month to a retirement plan for 25 years. Then you are able to increase the contribution to $500 per month for 20 years. Given a 9% interest rate, what is the value of your retirement plan after 45 years?
A) $1,743,956.03
B) $1,989,703.51
C) $2,189,194.36
D) $2,355,040.91

Accepted Answer

The answer of Assume that you contribute $300 per month...

Question 10

Teaser Rate Mortgage A mortgage broker is offering a 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 5 percent APR interest rate. After the second year, the mortgage interest charged increases to 8 percent APR. What is the effective interest rate in the first two years? What is the effective interest rate after the second year?
A) 4.89%, 7.72% respectively
B) 5.00%, 8.00% respectively
C) 5.12%, 8.30% respectively
D) 12.59%, 12.65% respectively

Accepted Answer

To find the effective interest rate in the first two years, we need to use the formula for annual percentage rate (APR) and compound interest:

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

Where r is the nominal interest rate, n is the number of compounding periods per year, and ^ denotes exponentiation.

For the first two years, r = 5% and n = 12, since the interest is compounded monthly. Plugging these values into the formula, we get:

APR = (1 + 0.05/12)^12 - 1 = 0.0512 or 5.12%

Therefore, the effective interest rate in the first two years is 5.12%.

After the second year, the interest rate increases to 8%, so we can use the same formula with r = 8% and n = 12 to find the new effective interest rate:

APR = (1 + 0.08/12)^12 - 1 = 0.0830 or 8.30%

Therefore, the effective interest rate after the second year is 8.30%.

The correct answer is C.

Question 11

What is the future value of a $500 annuity payment over 8 years if interest rates are 14%?
A) $6,241.09
B) $6,616.38
C) $6,750.14
D) $6,809.72

Accepted Answer

We can use the following formula to calculate the future value of an annuity payment:

FV = Pmt x [(1 + r)^n - 1] / r

where:
Pmt = annuity payment ($500)
r = interest rate (14% or 0.14)
n = number of payment periods (8)

FV = 500 x [(1 + 0.14)^8 - 1] / 0.14
FV = $6,616.38

Therefore, the best choice is B.

Question 12

A small business owner visits his bank to ask for a loan. The owner states that she can repay a loan at $2,500 per month for the next 2 years and then $3,000 per month for another 2 years after that. If the bank is charging customers 6.5% APR, how much would it be willing to lend the business owner?
A) $111,712.39
B) $114,009.21
C) $115,278.17
D) $117,809.63

Accepted Answer

The answer of A small business owner visits his bank...

Question 13

Given a 7% interest rate, compute the year 8 future value of deposits made in years 1, 2, 3, and 4 of $750, $1,200, $500, and $250.
A) $3,801.62
B) $3,899.17
C) $4,034.20
D) $4,167.29

Accepted Answer

To find the future value of each deposit, we compound each amount to year 8 using the formula FV = PV * (1 + r)^(n), where PV is the present value, r is the interest rate, and n is the number of years. For each deposit:  - Year 1: $750 * (1.07)^7 = $1,205.72  - Year 2: $1,200 * (1.07)^6 = $1,800.48  - Year 3: $500 * (1.07)^5 = $701.29  - Year 4: $250 * (1.07)^4 = $326.71  Adding these future values gives $4,034.20.

Question 14

Low Financing or Cash Back? A car company is offering a choice of deals. You can receive $2,000 cash back on the purchase, or a 2 percent APR, 3-year loan. The price of the car is $17,000 and you could obtain a 3-year loan from your credit union, at 7 percent APR. Which deal is cheaper?
A) The car company's 2 percent 3-year loan.
B) The rebate with the credit union's 7 percent 3-year loan.
C) Neither deal is cheaper.
D) There is not enough information given to determine which deal is cheaper.

Accepted Answer

The answer of Low Financing or Cash Back? A car...

Question 15

Future Value Given a 7 percent interest rate, compute the year 6 future value if deposits of $2,500 and $1,500 are made in years 2 and 3, respectively, and a withdrawal of $900 is made in year 4.
A) $2,721.44
B) $4,084.15
C) $4,491.60
D) $7,059.04

Accepted Answer

The answer of Future Value Given a 7 percent interest...

Question 16

Investing for Retirement Ross has decided that he wants to build enough retirement wealth that, if invested at 6 percent per year, will provide him with $2,500 monthly income for 30 years. To date, he has saved nothing, but he still has 20 years until he retires. How much money does he need to contribute per month to reach his goal?
A) $895.95
B) $902.47
C) $1,947.88
D) $2,500.00

Accepted Answer

To calculate the amount of money Ross needs to contribute per month, we can use the present value of an annuity formula:

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

where PV is the present value of the annuity, PMT is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, Ross wants a monthly payment of $2,500 for 30 years, or 360 months. The interest rate is 6% per year, compounded monthly, so r = 0.06/12 = 0.005. Ross has 20 years, or 240 months, to save. Therefore, we can calculate the present value of the annuity as follows:

PV = $2,500 x [(1 - (1 + 0.005/12)^(-12x30)) / (0.005/12)]
PV = $2,500 x [(1 - 0.32178) / 0.00041667]
PV = $2,500 x 54.76485
PV = $136,912.13

This means that Ross needs to save $136,912.13 by the time he retires in 20 years. To calculate the monthly payment he needs to make, we can rearrange the formula above:

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

PMT = $136,912.13 / [(1 - (1 + 0.005/12)^(-12x20)) / (0.005/12)]
PMT = $136,912.13 / 150.12442
PMT = $911.47

Therefore, Ross needs to contribute $911.47 per month for the next 20 years to reach his retirement goal. The closest answer choice is B, $902.47.

Question 17

Teaser Rate Mortgage A mortgage broker is offering a 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 5.5 percent APR interest rate. After the second year, the mortgage interest charged increases to 8.5 percent APR. What is the effective interest rate in the first two years? What is the effective interest rate after the second year?
A) 5.37%, 8.19% respectively
B) 5.50%, 8.50% respectively
C) 5.64%, 8.84% respectively
D) 12.60%, 12.66% respectively

Accepted Answer

The answer of Teaser Rate Mortgage A mortgage broker is...

Question 18

Compute the future value in year 12 of a $2,000 deposit in year 3 and another $4,000 deposit at the end of year 5 using a 10% interest rate.
A) $12,510.77
B) $12,909.81
C) $13,4067.31
D) $15,007.52

Accepted Answer

The correct answer is A because the future value of the $2,000 deposit in year 3 is $2,000 * (1 + 0.1)^9 = $3,310.01, and the future value of the $4,000 deposit at the end of year 5 is $4,000 * (1 + 0.1)^7 = $6,200.76. The total future value is $3,310.01 + $6,200.76 = $12,510.77.

Question 19

Future Value Given an 8 percent interest rate, compute the year 7 future value if deposits of $1,500 and $2,500 are made in years 2 and 3, respectively, and a withdrawal of $2,000 is made in year 5.
A) $1,909.42
B) $3,272.41
C) $3,433.60
D) $5,656.34

Accepted Answer

The answer of Future Value Given an 8 percent interest...

Question 20

If the future value of an ordinary, 11 year annuity is $5,575 and interest rates are 5.5%, what is the future value of the same annuity due?
A) $5,619.52
B) $5,769.06
C) $5,881.63
D) $5,947.88

Accepted Answer

The future value of an annuity due is higher than an ordinary annuity because payments are made at the beginning of each period. To find the future value of an annuity due, multiply the future value of the ordinary annuity by (1 + interest rate). Thus, $5,575 * (1 + 0.055) = $5,881.63.

Quiz 5: Time Value of Money 2: Analyzing Annuity Cash Flows

What is the present value of a $1,100 payment made every year forever when interest rates are 4.5%?

What is the present value of a $775 annuity payment over 6 years if interest rates are 11%?

Loan Balance Hank purchased a $20,000 car two years ago using an 8 percent, 5-year loan. He has decided that he would sell the car now, if he could get a price that would pay off the balance of his loan. What's the minimum price Hank would need to receive for his car?

Given an 8% interest rate, compute the present value of payments made in years 1, 2, 3 and 4 of $900, $800, $700, and $600.

If the present value of an ordinary, 8 year annuity is $12,500 and interest rates are 9.1%, what is the present value of the same annuity due?

A loan is offered with monthly payments and a 14.5% APR. What is the loan's effective annual rate (EAR) ?

Compute the present value of a $2,500 deposit in year 4 and another $10,000 deposit at the end of year 8 if interest rates are 15%.

Assume that you contribute $300 per month to a retirement plan for 25 years. Then you are able to increase the contribution to $500 per month for 20 years. Given a 9% interest rate, what is the value of your retirement plan after 45 years?

What is the future value of a $500 annuity payment over 8 years if interest rates are 14%?

A small business owner visits his bank to ask for a loan. The owner states that she can repay a loan at $2,500 per month for the next 2 years and then $3,000 per month for another 2 years after that. If the bank is charging customers 6.5% APR, how much would it be willing to lend the business owner?

Given a 7% interest rate, compute the year 8 future value of deposits made in years 1, 2, 3, and 4 of $750, $1,200, $500, and $250.

Low Financing or Cash Back? A car company is offering a choice of deals. You can receive $2,000 cash back on the purchase, or a 2 percent APR, 3-year loan. The price of the car is $17,000 and you could obtain a 3-year loan from your credit union, at 7 percent APR. Which deal is cheaper?

Future Value Given a 7 percent interest rate, compute the year 6 future value if deposits of $2,500 and $1,500 are made in years 2 and 3, respectively, and a withdrawal of $900 is made in year 4.

Compute the future value in year 12 of a $2,000 deposit in year 3 and another $4,000 deposit at the end of year 5 using a 10% interest rate.

Future Value Given an 8 percent interest rate, compute the year 7 future value if deposits of $1,500 and $2,500 are made in years 2 and 3, respectively, and a withdrawal of $2,000 is made in year 5.

If the future value of an ordinary, 11 year annuity is $5,575 and interest rates are 5.5%, what is the future value of the same annuity due?