Question 1

Keith Stone has a 10-year old daughter, Kate, who will be entering college in 8 years.Keith estimates college costs to be $16,000, $17,000, $18,000 and $19,000 payable at the beginning of each of Kate's four years in college.How much must Keith save each year (assume end of year payments) for each of the next 8 years to have enough savings to pay for Kate's education? Assume Keith can earn 9% on his savings.

Accepted Answer

Year Present Value
1 $16,000(1.000) = $16,000
2 17,000(0.917) = 15,589
3 18,000(0.842) = 15,156
4 19,000(0.772) = 14,668
$61,413
PMT = $61,413/11.028 = $5,569

Question 2

If a 16 year old high school student put $2,000 at the end of each year for 4 years into an IRA that earned a rate of 9%, how much would she have accumulated by age 65? Assume funds are left to accumulate for 45 years (age 20 - 65) at 9%.

Accepted Answer

Solution using a calculator:
PART I N = 4
I = 9
PMT = -$2,000
Solve for FV = $9,146.26
PART II N = 45
I = 9
PV = -$9,146.26
Solve for FV = $442,014

Question 3

Cosmos Touring wishes to replace its luxury bus in 10 years by accumulating funds in a special account.The new bus is expected to cost $180,000.How much must Cosmos put into the fund in equal, end-of-year amounts if earnings are expected to be 8% for the first 4 years and 10% thereafter?

Accepted Answer

$180,000 = PMT(4.506)(1.772) + PMT(7.716)
$180,000 = PMT(15.7006) PMT = $11,465

Question 4

What is the present value of the following mixed cash flow stream if interest is 6% (rounded)?
$$\begin{array} { | l | l | } 
\hline Y A A R & \text { QASH FLOW } \
\hline 1 & \$ 5,000 \
\hline 2 & 40,000 \
\hline 3 & \$ 9,500 \
\hline
\end{array}$$

Accepted Answer

Solution using a calculator:
CF₀ = 0
CF₁ = 5,000
CF₂ = 8,000
CF₃ = 9,500
I = 6
Solve for NPV = $19,813 by calculator.

Question 5

When you purchased a car, you borrowed $20,000 from the bank at 9.20% and agreed to make monthly payments for 3 years.What is your monthly payment?

Accepted Answer

Solution using a calculator:
N = 3 × 12 = 360
I = 9.20 ÷ 12 = .7666...
PV = -$20,000
Solve for PMT = $637.86
$637.86 by calculator

Question 6

You wish to have $10,000 per year as a retirement supplement for 20 years (from age 65-85).You are now 40 years old.How much must you save each year for the next 25 years if you assume your savings will earn 12% annually?

Accepted Answer

The correct answer is A. $560.17.To calculate the present value of the future retirement supplement, we can use the formula:PV = FV / (1 + r)^nwhere:PV is the present valueFV is the future valuer is the annual interest raten is the number of yearsIn this case, we have:FV = $10,000r = 12%n = 20Plugging these values into the formula, we get:PV = $10,000 / (1 + 0.12)^20PV = $10,000 / 13.686PV = $730.94This is the amount of money that we need to have saved by the time we retire in order to generate $10,000 per year for 20 years.To calculate how much we need to save each year for the next 25 years, we can use the formula:PMT = PV * (r / ((1 + r)^n - 1))where:PMT is the annual paymentPV is the present valuer is the annual interest raten is the number of yearsIn this case, we have:PV = $730.94r = 12%n = 25Plugging these values into the formula, we get:PMT = $730.94 * (0.12 / ((1 + 0.12)^25 - 1))PMT = $730.94 * (0.12 / 10.384)PMT = $560.17Therefore, we need to save $560.17 each year for the next 25 years in order to have $10,000 per year as a retirement supplement for 20 years.

Question 7

Al Corbin is 25 years old today and he wishes to accumulate enough money over the next 35 years to provide for a 20 year retirement annuity of $100,000 at the beginning of each year, starting with his 60th birthday.He can save $2,000 at the end of each of the next 10 years and $3,000 each year for the following 10 years.How much must he save each year at the end of years 21 through 35 to obtain his goal? Assume that the average rate of return over the entire period will be 10%.

Accepted Answer

PVAN = $100,000(8.514)(1.10) = $936,540
$936,540 = $2,000(15.937)(10.835) + $3,000(15.937)(4.177) + PMT(31.772)
$936,540 = $345,355 + $199,707 + 31.772PMT PMT = $12,321

Question 8

The Summer Breeze Hotel borrowed $100,000 from the Meadowlands Bank to pay for a new air conditioning system.The loan is for a period of 5 years at an interest rate of 10% and requires 5 equal end-of-year payments that include both principal and interest on the outstanding balance.What will be the outstanding balance after the third payment?

Accepted Answer

The answer of The Summer Breeze Hotel borrowed $100,000 from...

Question 9

Your monthly statement from your bank credit card shows that the monthly rate of interest is 1.5%.What is the annual effective rate of interest you are being charged on your credit card?

Accepted Answer

iₑff = (1 + 0.18/12)¹² - 1 = .1956 or 19.56%

Question 10

Inco purchased a computer for $200,000 and this machine is expected to generate annual cash flows of $48,271 over the next 5 years.What is the expected rate of return on this investment?

Accepted Answer

Solution using a calculator:
N = 5
PV = -$200,000 PMT = $48,271
Solve for I = 6.61%

Question 11

1st Bank offers you a car loan at an annual interest rate of 10% compounded monthly.What effective annual interest rate is the bank charging you?

Accepted Answer

iₑff = (1 + 0.10/12)¹² - 1 = .1047 or 10.47%

Question 12

Assume you purchased a home and borrowed $100,000 at a rate of 8% compounded monthly over 30 years.What is your monthly payment?

Accepted Answer

Solution using a calculator:
PV = -$100,000
I = 8 ÷ 12 = .6666...
N = 30 × 12 = 360
Solve for PMT
$733.76 by calculator

Question 13

What monthly rate of interest will yield an annual effective rate of interest of 14%?

Accepted Answer

The answer of What monthly rate of interest will yield...

Question 14

Which of the following statements is/are correct?

Accepted Answer

Solution using a calculator:
CF₀ = 0
CF₁ = 400
CF₂ = 600
CF₃ = 800
I = 6
Solve for NPV = $1,583.05 by calculator Calculator should be in END mode
N= 4 (An annuity due earns one extra year of interest) I = 6
PV = -1,583.05
Solve for FV = $1,998.57 by calculator

Question 15

Based on the Rule of 72, what interest rate do you need to earn to double your money in 6 years?

Accepted Answer

The Rule of 72 states that dividing 72 by the interest rate will give you the number of years it takes to double your money. Therefore, 72 divided by 6 (the desired number of years) equals 12% (the necessary interest rate). So, option B is the correct answer.

Question 16

What is the present value of the following net cash flows if the discount rate is 10%?
$$\begin{array} { l l } 
\text { Year } & \text { Net Cash Flow } \
1 - 10 & \$ 20,000 \text { each year } \
11 - 15 & \$ 15,000 \text { each year } \
16 - 20 & \$ 10,000 \text { each year }
\end{array}$$

Accepted Answer

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

Question 17

When you purchased a car, you borrowed $20,000 from the bank and agreed to make monthly payments of $423.17 for 5 years.What rate of interest is the bank charging you?

Accepted Answer

Solution using a calculator:
N = 5 × 12
PV = -$20,000 PMT = $423.17
Solve for I = .818 × [12 (convert to annual)] = 9.82%
9.82% by calculator

Question 18

What is the present value of $1,000 received 2 years from today if the nominal interest rate is 9% and compounded monthly?

Accepted Answer

PV = $1,000/(1 + .09/12)¹²×² = $836

Question 19

If your parents put $2,000 a year into an IRA account for you in each of your last 4 teenage years (age 16,17,18, and 19), how much would the IRA account have in it at your retirement 45 years later if the account earned 12% each year? (Assume end-of-year payments.)

Accepted Answer

FV = 2000(4.779)(93.051)(1.765) = $1,569,758

Question 20

What is the value in 10 years of $10,000 deposited in an account earning 8% compounded monthly?

Accepted Answer

FV = 10,000(1 + .08/12 )¹²×¹⁰ = $22,285

Quiz 5: The Time Value of Money