Question 1

What annual interest rate would you need to earn if you wanted a $500 per month contribution to grow to $27,050 in four years?
A) 2.37 percent
B) 5.77 percent
C) 6.00 percent
D) 13.53 percent

Accepted Answer

The correct answer is C because the annual interest rate needed to earn $500 per month contribution to grow to $27,050 in four years is 6.00 percent.

Question 2

Given a 6 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,200, $1,400, $1,400, and $1,500.
A) $4,356.52
B) $4,741.68
C) $5,188.68
D) $5,506.00

Accepted Answer

The present value of each deposit is calculated using the formula PV = FV / (1 + r)^n. Summing these values gives the total present value: $1,200/(1.06)^1 + $1,400/(1.06)^2 + $1,400/(1.06)^3 + $1,500/(1.06)^4 = $4,741.68.

Question 3

What is the interest rate of a 4-year, annual $1,000 annuity with present value of $3,500?
A) 3.85 percent
B) 5.56 percent
C) 8.84 percent
D) 9.70 percent

Accepted Answer

The present value of an annuity can be calculated using the formula PV = PMT * [(1 - (1 + r)^-n) / r], where PV is the present value, PMT is the annual payment, r is the interest rate per period, and n is the number of periods. Given PV = $3,500, PMT = $1,000, and n = 4, we can solve for r, which gives us an interest rate of approximately 5.56 percent.

Question 4

Payday loans are very short-term loans that charge very high interest rates. You can borrow $200 today and repay $250 in two weeks. What is the compound annual rate implied by this 25 percent rate charged for only two weeks?
A) 26.60 percent
B) 32,987.22 percent
C) 30.00 percent
D) 128.25 percent

Accepted Answer

The compound annual rate (CAR) for a payday loan that charges 25% for two weeks can be calculated using the formula for compound interest, taking into account the number of compounding periods in a year. Given the short-term nature of the loan (two weeks), the annualization of the interest rate significantly increases it, leading to a very high CAR, which in this case is 32,987.22 percent. This reflects the exponential growth of interest due to frequent compounding over the year.

Question 5

A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $1,500 per month for the next three years and then $500 per month for the two years after that. If the bank is charging customers 5.5 percent APR, how much would it be willing to lend the business owner?
A) $4,046.90
B) $59,293.50
C) $24,261.00
D) $66,000.00

Accepted Answer

The bank would calculate the present value of the loan repayments using the given APR. The present value of the first three years of payments ($1,500 per month) and the next two years of payments ($500 per month) at a 5.5% annual interest rate would be approximately $59,293.50.

Question 6

A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $2,000 per month for the next three years and then $1,000 per month for the two years after that. If the bank is charging customers 8.5 percent APR, how much would it be willing to lend the business owner?
A) $80,419.29
B) $6,494.66
C) $21,780.74
D) $96,000.00

Accepted Answer

The loan amount can be calculated using the present value of an annuity formula, which considers the monthly payments, the interest rate, and the duration of the loan. The calculation involves two parts due to the change in payment amount after three years. First, calculate the present value of $2,000 monthly payments for three years (36 months), and then calculate the present value of $1,000 monthly payments for the following two years (24 months). Finally, sum these two present values to find the total amount the bank would be willing to lend. The correct calculation results in a total of approximately $80,419.29, making option A the correct answer.

Question 7

Given a 7 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,500, and $1,500.
A) $3,967.06
B) $4,351.50
C) $4,859.81
D) $5,207.00

Accepted Answer

The present value of each deposit 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. Calculating for each deposit and summing them gives $4,351.50.

Question 8

A perpetuity pays $50 per year and interest rates are 9 percent. How much would its value change if interest rates decreased to 6 percent?
A) $150.00 increase
B) $150.00 decrease
C) $277.78 increase
D) $277.78 decrease

Accepted Answer

The value of a perpetuity is calculated as the annual payment divided by the interest rate. At 9%, the value is $50 / 0.09 = $555.56. At 6%, the value is $50 / 0.06 = $833.33. The difference is $833.33 - $555.56 = $277.77, which rounds to $277.78 increase.

Question 9

You wish to buy a $15,000 car. The dealer offers you a 4-year loan with a 9 percent APR. What are the monthly payments?
A) $260.78
B) $312.50
C) $373.28
D) $3,820.56

Accepted Answer

To calculate the monthly payment, use the formula for an amortizing loan: M = P[r(1+r)^n]/[(1+r)^n – 1], where P is the principal ($15,000), r is the monthly interest rate (0.09/12), and n is the total number of payments (4*12). This calculation results in approximately $373.28.

Question 10

What annual interest rate would you need to earn if you wanted a $200 per month contribution to grow to $14,700 in five years?
A) 6.47 percent
B) 7.76 percent
C) 8.01 percent
D) 14.70 percent

Accepted Answer

The answer of What annual interest rate would you need...

Question 11

Joey realizes that he has charged too much on his credit card and has racked up $3,000 in debt. If he can pay $150 each month and the card charges 18 percent APR (compounded monthly), how long will it take him to pay off the debt?
A) 13.03 months
B) 14.68 months
C) 20.00 months
D) 23.96 months

Accepted Answer

To calculate the time it will take Joey to pay off his credit card debt, we use the formula for the payment on an installment loan: $ P = \frac{rPV}{1 - (1 + r)^{-n}} $, where P is the payment, r is the monthly interest rate, PV is the present value of the loan (or initial amount of debt), and n is the number of payments. Rearranging the formula to solve for n gives us $ n = \frac{\log(P) - \log(P - rPV)}{\log(1 + r)} $. Given that the APR is 18%, the monthly interest rate is $ \frac{18\%}{12} = 1.5\% = 0.015 $. Plugging in the values: $ P = 150 $, $ r = 0.015 $, and $ PV = 3000 $, we can solve for n. This calculation shows that it will take Joey approximately 23.96 months to pay off the debt, assuming he makes consistent monthly payments of $150 and the interest is compounded monthly.

Question 12

If you start making $25 monthly contributions today and continue them for four years, what is their future value if the compounding rate is 6 percent APR? What is the present value of this annuity?
A) $101.26, $99.26
B) $1,352.45, $1,064.51
C) $1,359.21, $1,069.83
D) $2,171.02, $1,516.03

Accepted Answer

The future value of an annuity formula is used to calculate the future value of the monthly contributions compounded at 6% APR over four years. The present value of an annuity formula is used to calculate the present value of these contributions.

Question 13

A perpetuity pays $100 per year and interest rates are 6.5 percent. How much would its value change if interest rates increased to 9 percent?
A) $250.00 increase
B) $250.00 decrease
C) $427.35 increase
D) $427.35 decrease

Accepted Answer

The value of a perpetuity is calculated using the formula $ \text{Value} = \frac{PMT}{r} $, where PMT is the annual payment and r is the interest rate. Initially, the value is $ \frac{100}{0.065} = $1,538.46 $. If the interest rate increases to 9%, the new value is $ \frac{100}{0.09} = $1,111.11 $. The difference is $1,538.46 - $1,111.11 = $427.35, indicating a decrease in value.

Question 14

Given a 4 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,400.
A) $4,103.06
B) $4,334.53
C) $4,615.38
D) $4,804.00

Accepted Answer

The present value (PV) of each deposit 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. Calculating each deposit: Year 1: $1,000 / (1.04)^1 = $961.54, Year 2: $1,200 / (1.04)^2 = $1,110.68, Year 3: $1,200 / (1.04)^3 = $1,067.00, Year 4: $1,400 / (1.04)^4 = $1,195.31. Adding these gives a total present value of $4,334.53.

Question 15

Payday loans are very short-term loans that charge very high interest rates. You can borrow $600 today and repay $675 in two weeks. What is the compound annual rate implied by this 12.5 percent rate charged for only two weeks?
A) 12.89 percent
B) 13.28 percent
C) 2037.79 percent
D) 113.28 percent

Accepted Answer

The compound annual rate (CAR) can be calculated using the formula for compound interest, taking into account the short duration (2 weeks) and annualizing it. The calculation involves finding the effective annual rate for a 12.5% interest rate over a 2-week period, compounded weekly. Given the dramatic increase when compounded over 52 weeks/year, the CAR is significantly higher than the simple interest rate, leading to an answer of 2037.79 percent.

Question 16

You wish to buy a $20,000 car. The dealer offers you a 5-year loan with an 8 percent APR. What are the monthly payments?
A) $272.19
B) $333.33
C) $405.53
D) $4,080.35

Accepted Answer

To calculate the monthly payment for a loan, you can use the formula for a fixed-rate loan which is often represented as $PMT = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$, where $P$ is the principal amount ($20,000), $r$ is the monthly interest rate (annual rate divided by 12, so 0.08/12 = 0.0066667), and $n$ is the total number of payments (5 years x 12 months = 60 payments). Plugging these values into the formula gives a monthly payment of approximately $405.53.

Question 17

If you start making $100 monthly contributions today and continue them for five years, what is their future value if the compounding rate is 10 percent APR? What is the present value of this annuity?
A) $508.14, $487.74
B) $512.64, $491.80
C) $7,743.71, $4,706.53
D) $7,808.24, $4,745.76

Accepted Answer

The future value of an annuity formula is used to calculate the future value of the monthly contributions compounded at 10% annually over five years. The present value of an annuity formula is used to calculate the present value of these contributions.

Question 18

Given a 5 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,400, $1,400, and $1,500.
A) $4,360.32
B) $4,665.65
C) $5,047.62
D) $5,305.00

Accepted Answer

The present value (PV) of each deposit can be calculated using the formula PV = FV / (1 + r)^n, where FV is the future value of the deposit, r is the annual interest rate, and n is the number of years until the deposit is made. For each deposit:- Year 1: PV = $1,000 / (1 + 0.05)^1 = $952.38- Year 2: PV = $1,400 / (1 + 0.05)^2 = $1,269.31- Year 3: PV = $1,400 / (1 + 0.05)^3 = $1,208.17- Year 4: PV = $1,500 / (1 + 0.05)^4 = $1,235.79Adding these values together gives the total present value of the deposits: $952.38 + $1,269.31 + $1,208.17 + $1,235.79 = $4,665.65.

Question 19

Payday loans are very short-term loans that charge very high interest rates. You can borrow $500 today and repay $550 in two weeks. What is the compound annual rate implied by this 10 percent rate charged for only two weeks?
A) 10.50 percent
B) 12.00 percent
C) 1091.82 percent
D) 110.50 percent

Accepted Answer

The compound annual rate (CAR) can be calculated using the formula for compound interest, taking into account the short duration of the loan (2 weeks) and annualizing it. Given the 10% interest for 2 weeks, the annual rate is much higher when compounded weekly over a year, leading to a CAR of approximately 1091.82%.

Question 20

What is the interest rate of a 6-year, annual $3,000 annuity with present value of $14,000?
A) 5.64 percent
B) 7.69 percent
C) 10.17 percent
D) 11.32 percent

Accepted Answer

The interest rate can be found using the formula for the present value of an annuity: $PV = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where PV is the present value, PMT is the annual payment, r is the interest rate per period, and n is the number of periods. Plugging in the given values ($14,000 for PV, $3,000 for PMT, and 6 for n) and solving for r requires trial and error or a financial calculator. The correct interest rate that satisfies this equation is approximately 7.69 percent.

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

What annual interest rate would you need to earn if you wanted a $500 per month contribution to grow to $27,050 in four years?

Given a 6 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,200, $1,400, $1,400, and $1,500.

What is the interest rate of a 4-year, annual $1,000 annuity with present value of $3,500?

Payday loans are very short-term loans that charge very high interest rates. You can borrow $200 today and repay $250 in two weeks. What is the compound annual rate implied by this 25 percent rate charged for only two weeks?

Given a 7 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,500, and $1,500.

A perpetuity pays $50 per year and interest rates are 9 percent. How much would its value change if interest rates decreased to 6 percent?

You wish to buy a $15,000 car. The dealer offers you a 4-year loan with a 9 percent APR. What are the monthly payments?

What annual interest rate would you need to earn if you wanted a $200 per month contribution to grow to $14,700 in five years?

Joey realizes that he has charged too much on his credit card and has racked up $3,000 in debt. If he can pay $150 each month and the card charges 18 percent APR (compounded monthly) , how long will it take him to pay off the debt?

If you start making $25 monthly contributions today and continue them for four years, what is their future value if the compounding rate is 6 percent APR? What is the present value of this annuity?

A perpetuity pays $100 per year and interest rates are 6.5 percent. How much would its value change if interest rates increased to 9 percent?

Given a 4 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,400.

Payday loans are very short-term loans that charge very high interest rates. You can borrow $600 today and repay $675 in two weeks. What is the compound annual rate implied by this 12.5 percent rate charged for only two weeks?

You wish to buy a $20,000 car. The dealer offers you a 5-year loan with an 8 percent APR. What are the monthly payments?

If you start making $100 monthly contributions today and continue them for five years, what is their future value if the compounding rate is 10 percent APR? What is the present value of this annuity?

Given a 5 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,400, $1,400, and $1,500.

Payday loans are very short-term loans that charge very high interest rates. You can borrow $500 today and repay $550 in two weeks. What is the compound annual rate implied by this 10 percent rate charged for only two weeks?

What is the interest rate of a 6-year, annual $3,000 annuity with present value of $14,000?