Question 1

Isaac realizes that he charged too much on his credit card and has racked up $7,000 in debt.If he can pay $275 each month and the card charges 17.55 percent APR (compounded monthly),how long will it take him to pay off the credit card? How much interest expense will Isaac pay during this time?
A) 32.07 months; $8,819.25
B) 32.07 months; $1,819.25
C) 22.07 months; $8,819.25
D) 22.07 months; $1,819.25

Accepted Answer

Step 1: PV = 7000, PMT = 275, FV = 0, I = 17.55/12, => N = 32.07.
Step 2: (32.07 × 275) − 7000 = 3819.25.

Question 2

A mortgage broker is offering a $225,000 30-year mortgage with a teaser rate.In the first two years of the mortgage,the borrower makes monthly payments on only a 2.5 percent APR interest rate.After the second year,the mortgage interest rate charged increases to 8.5 percent APR.What are the mortgage payments in the first two years? What are the mortgage payments after the second year?
A) $790.25; $1,512.93
B) $790.25; $1,309.13
C) $889.02; $1,650.61
D) $889.02; $1,677.09

Accepted Answer

Step 1: N = 360, I = 2.5/12, PV = 225000, FV = 0, PMT = 889.02.
Step 2: N = 24, I = 2.5/12, PMT = 889.02, PV = 225000, => FV = 214668.13.
Step 3: PV = 214668.13, N = 336, I = 8.5/12, FV = 0, => PMT = 1677.09.

Question 3

Consider that you are 30 years old and have just changed to a new job.You have $91,000 in the retirement plan from your former employer.You can roll that money into the retirement plan of the new employer.You will also contribute $400 each month into your new employer's plan.If the rolled-over money and the new contributions both earn a 7 percent annual return,how much should you expect to have when you retire in 38 years?
A) $2,019,095.26
B) $2,195,145.40
C) $2,298,025.12
D) $2,301,116.92

Accepted Answer

PV = 91000, N = 456, I = 7/12, PMT = 400, => FV = 2195145.40

Question 4

Chase purchased a $23,000 car three years ago using a 14 percent,6-year car 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 is the minimum price Chase would need to receive for his car? (Assume monthly payments.)
A) $12,592.41
B) $13,866.82
C) $14,136.72
D) $14,809.48

Accepted Answer

Step 1: PV = 23000, FV = 0, N = 72, I − 14/12, => PMT = 473.93.
Step 2: PV = 23000, N = 36, I = 14/12, PMT = −473.93, => FV = 13866.82.

Question 5

What is the interest rate of a 6-year,annual $10,000 annuity with a present value of $40,000?
A) 11.94 percent
B) 12.24 percent
C) 12.98 percent
D) 13.12 percent

Accepted Answer

PV = 40,000, PMT = 10,000, FV = 0, N = 6, => I = 12.98

Question 6

If you start making $115 monthly contributions today and continue them for six years,what is their present value if the compounding rate is 12 percent APR? What is the present value of this annuity?
A) $5,512.90
B) $5,633.10
C) $5,882.30
D) $5,941.12

Accepted Answer

Set BEG mode. PMT = 115, N = 72, I = 1, FV = 0, => PV = 5941.12

Question 7

What annual interest rate would you need to earn if you wanted a $1,250 per month contribution to grow to $65,000 in three years?
A) 18.59 percent
B) 21.26 percent
C) 24.00 percent
D) 25.19 percent

Accepted Answer

PV = 0; N = 36, PMT = 1250, FV = 65000, => I = 2.00 annual rate = 2 × 12 = 24

Question 8

A perpetuity pays $250 per year and interest rates are 8.5 percent.How much would its value change if interest decreased to 5.5 percent? Did the value increase or decrease?
A) $1,604.27; increase
B) $1,604.27; decrease
C) $1,714.20; increase
D) $1,714.20; decrease

Accepted Answer

Step 1: 250/0.085 = 2941.18.
Step 2: 250/0.055 = 4545.45.
Step 3: Difference = 1604.27.

Question 9

You wish to buy a $30,000 car.The dealer offers you a 5-year loan with a 9 percent APR.What are the monthly payments? What is the monthly payment if you paid interest only?
A) $622.75, $225.00
B) $659.41, $291.23
C) $701.23, $291.23
D) $712.03, $271.19

Accepted Answer

Step 1: PV = 30,000, N = 60, I = 9/12, FV = 0, => PMT = 622.75.
Step 2: PV = 30000, N = 60, I = 9/12, FV = −30000, => PMT = 225.00.

Question 10

Payday loans are very short-term loans that charge very high interest rates.You can borrow $550 today and repay $675 in two weeks.What is the compounded annual rate implied by this 22.73 percent rate charged for only two weeks?
A) 25.40 percent
B) 204.45 percent
C) 2,044.56 percent
D) 20,445.61 percent

Accepted Answer

[(1 + 0.2273)^26] − 1 = 204.4561 = 20445.61 percent.

Question 11

A furniture company is offering a choice of deals.You can receive $100 cash back on the purchase,or a 2 percent APR,2-year loan.The price of the dining room set is $3,750 and you could obtain a 2-year loan from your credit union at 6 percent APR.What is the cost per month of each deal?
A) Cash back: $161.77, 2 percent APR: $159.53
B) Cash back: $171.29, 2 percent APR: $179.02
C) Cash back: $153.96, 2 percent APR: $181.09
D) Cash back: $180.03, 2 percent APR: $166.17

Accepted Answer

Step 1: Cash back: PV = 3650, N = 24, I = 6/12; FV = 0, => PMT = 161.77.
Step 2: 2 percent APR: PV = 3750, N = 24, I = 2/12, FV = 0, PMT = 159.53.

Question 12

What is the amount of interest and repayment of principal balance in month 2 for a loan of $10,000,paid monthly over five years at a 7 percent APR?
A) Interest = $101.32, Principal repayment = $57.51
B) Interest = $57.52, Principal repayment = $140.49
C) Interest = $157.52, Principal repayment = $40.49
D) Interest = $107.52, Principal repayment = $40.49

Accepted Answer

Step 1: PV = 10000, N = 60, I = 7/12, FV = 0, => PMT = 198.01.
Step 2: N = 1, PV = 10000, PMT = −198.01, I = 7/12, => FV = 9860.32.
Step 3: Int = 9860.32 × 0.07/12 = 57.52.
Step 4: 198.01 − 57.52 = Repayment = 140.49.

Question 13

Jasmine has decided that she wants to build enough retirement wealth that,if invested at 6 percent per year,will provide her with $3,000 of monthly income for 30 years.To date,she has saved nothing but she still has 25 years until she retires.Jasmine believes that she can earn 6 percent on her investments until she retires.How much money does she need to contribute per month to reach her goal?
A) $512.93
B) $616.27
C) $722.05
D) $863.49

Accepted Answer

Step 1: FV = 0, PMT = 3000, N = 360, I = 6/12, PV = 500374.84.
Step 2: PV = 0, FV = 500374.84, N = 300, I = 6/12, => PMT = 722.05.

Question 14

A car company is offering a choice of deals.You can receive $600 cash back on the purchase,or a 2 percent APR,4-year loan.The price of the car is $18,900 and you could obtain a 4-year loan from your credit union at 6 percent APR.What is the monthly payment of each deal?
A) cash back: PMT = $429.78, 2 percent APR: PMT = $410.04
B) cash back: PMT = $438.24, 2 percent APR: PMT = $424.09
C) cash back: PMT = $458.12, 2 percent APR: PMT = $414.09
D) cash back: PMT = $408.33, 2 percent APR: PMT = $410.04

Accepted Answer

Step 1: PV= 18300, FV = 0, I = 6/12, N = 48, => PMT = 429.78.
Step 2: PV = 18900, FV = 0, I = 2/12, N = 48, => PMT = 410.04.

Question 15

Isaac realizes that he charged too much on his credit card and has racked up $5,000 in debt.If he can pay $225 each month and the card charges 17.55 percent APR (compounded monthly),how long will it take him to pay off the credit card?
A) 19.14 months
B) 21.77 months
C) 22.62 months
D) 27.07 months

Accepted Answer

PV = 5000, PMT = 225, FV = 0, I = 17.55/12, => N = 27.07

Question 16

Consider that you are 30 years old and have just changed to a new job.You have $91,000 in the retirement plan from your former employer.You can roll that money into the retirement plan of the new employer.You will also contribute $4,800 each year into your new employer's plan.If the rolled-over money and the new contributions both earn a 7 percent return,how much should you expect to have when you retire in 38 years?
A) $2,012,560.60
B) $2,018,506.60
C) $2,106,718.60
D) $2,216,781.60

Accepted Answer

PV = 91000, I = 7, PMT = 4800, N = 38, => FV = 2018506.60

Question 17

Jasmine has decided that she wants to build enough retirement wealth that,if invested at 6 percent per year,will provide her with $3,000 of monthly income for 30 years.To date,she has saved nothing but she still has 25 years until she retires.Jasmine believes that she can earn 9 percent on her investments until she retires.How much money does she need to contribute per month to reach her goal?
A) $446.32
B) $521.84
C) $667.13
D) $722.05

Accepted Answer

Step 1: FV = 0, PMT = 3000, N = 360, I = 6/12, PV = 500374.84.
Step 2: PV = 0, FV = 500374.84, N = 300, I = 9/12, => PMT = 446.32.

Question 18

Chase purchased a $30,000 car three years ago using a 10 percent,5-year car 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 is the minimum price Chase would need to receive for his car? (Assume monthly payments.)
A) $12,000.00
B) $13,813.25
C) $21,500.75
D) $23,739.05

Accepted Answer

Step 1: PV = 30000, FV = 0, N = 60, I − 10/12, => PMT = 637.4113.
Step 2: PV = 30000, N = 36, I = 10/12, PMT = −637.4113, => FV = 13813.2487.

Question 19

Given a 10 percent interest rate,compute the year 9 future value if deposits of $10,000 and $20,000 are made in years 1 and 5 respectively,and a withdrawal of $5,000 is made in year 7.
A) $44,667.89
B) $45,103.47
C) $46,585.66
D) $47,002.89

Accepted Answer

Step 1: PV= 10,000, N = 8, I = 10, PMT= 0, => FV = 21435.89.
Step 2: PV = 20000, N = 4, I = 10, PMT = 0, => FV = 29282.00.
Step 3: PV = −5000, PMT = 0, N = 2, I = 10, => FV = −6050.00. sum of FVs = 44,667.89

Question 20

A perpetuity pays $250 per year and interest rates are 5.5 percent.How much would its value change if interest increased to 8.5 percent? Did the value increase or decrease?
A) $1,604.27; increase
B) $1,604.27; decrease
C) $1,508.29; increase
D) $1,508.29; decrease

Accepted Answer

Step 1: 250/0.055 = 4545.45.
Step 2: 250/0.085 = 2941.18.
Step 3: Difference = −1604.27.

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

Isaac realizes that he charged too much on his credit card and has racked up $7,000 in debt.If he can pay $275 each month and the card charges 17.55 percent APR (compounded monthly) ,how long will it take him to pay off the credit card? How much interest expense will Isaac pay during this time?

Chase purchased a $23,000 car three years ago using a 14 percent,6-year car 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 is the minimum price Chase would need to receive for his car? (Assume monthly payments.)

What is the interest rate of a 6-year,annual $10,000 annuity with a present value of $40,000?

If you start making $115 monthly contributions today and continue them for six years,what is their present value if the compounding rate is 12 percent APR? What is the present value of this annuity?

What annual interest rate would you need to earn if you wanted a $1,250 per month contribution to grow to $65,000 in three years?

A perpetuity pays $250 per year and interest rates are 8.5 percent.How much would its value change if interest decreased to 5.5 percent? Did the value increase or decrease?

You wish to buy a $30,000 car.The dealer offers you a 5-year loan with a 9 percent APR.What are the monthly payments? What is the monthly payment if you paid interest only?

Payday loans are very short-term loans that charge very high interest rates.You can borrow $550 today and repay $675 in two weeks.What is the compounded annual rate implied by this 22.73 percent rate charged for only two weeks?

A furniture company is offering a choice of deals.You can receive $100 cash back on the purchase,or a 2 percent APR,2-year loan.The price of the dining room set is $3,750 and you could obtain a 2-year loan from your credit union at 6 percent APR.What is the cost per month of each deal?

What is the amount of interest and repayment of principal balance in month 2 for a loan of $10,000,paid monthly over five years at a 7 percent APR?

A car company is offering a choice of deals.You can receive $600 cash back on the purchase,or a 2 percent APR,4-year loan.The price of the car is $18,900 and you could obtain a 4-year loan from your credit union at 6 percent APR.What is the monthly payment of each deal?

Isaac realizes that he charged too much on his credit card and has racked up $5,000 in debt.If he can pay $225 each month and the card charges 17.55 percent APR (compounded monthly) ,how long will it take him to pay off the credit card?

Chase purchased a $30,000 car three years ago using a 10 percent,5-year car 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 is the minimum price Chase would need to receive for his car? (Assume monthly payments.)

Given a 10 percent interest rate,compute the year 9 future value if deposits of $10,000 and $20,000 are made in years 1 and 5 respectively,and a withdrawal of $5,000 is made in year 7.

A perpetuity pays $250 per year and interest rates are 5.5 percent.How much would its value change if interest increased to 8.5 percent? Did the value increase or decrease?