Question 1

You plan to lease a Saab automobile that sells for $22,657 and has no salvage value.If the monthly lease is $499, with the first of 60 payments due immediately.What is the implied annual interest rate on your lease?

Accepted Answer

The implied annual interest rate can be calculated using the present value of an annuity formula. Given the monthly payment, the number of payments, and the present value (car price), the interest rate that equates these is approximately 12%.

Question 2

Jackie plans to open her own book store in 10 years.To raise the "seed" money she has committed $10,000 she now has in a mutual fund.In addition, she plans to save $2,000 per year (end of year) for the next 5 years and $3,000 per year (end of year) for the following 5 years.How much "seed" money will Jackie have in 10 years if the investments earn 10 percent per year compounded annually?

Accepted Answer

FV = $10,000(2.594) + $2,000(6.105)(1.611) + $3,000(6.105) = $63,925

Question 3

If the discount rate is 12%, what is the present value of the following cash flows:
$$\begin{array} { l c } 
\text { Year } & \text { Cash Flow } \
1 & \$ 10,000 \
2 & \$ 11,000 \
3 & \$ 12,000 \
4 & \$ 13,000 \
5 & \$ 14,000 \
6 - 15 & \$ 15,000 \text { each year }
\end{array}$$

Accepted Answer

The answer of If the discount rate is 12%, what...

Question 4

You wish to save $500,000 in the next 25 years.You notice that a corporate bond fund earns about 11 percent per year and that is where you put your savings.How much must you save each year to obtain your goal?

Accepted Answer

To find the annual savings required, we use the future value of an annuity formula: FV = Pmt * [(1 + r)^n - 1] / r. Here, FV = $500,000, r = 0.11, and n = 25. Solving for Pmt gives approximately $4,370.13.

Question 5

Seebee makes quarterly (end of period) payments of $30,000 into a pension fund earning 12 percent per year compounded quarterly for 10 years.How much interest will they have earned in 10 years?

Accepted Answer

FVAN₄₀ = $30,000(75.401) = $2,262,030
Fund balance after 10 years of $2,262,030 less Payments of $1,200,000 results in Interest =
$1,062,030

Question 6

How much will you have at the end of 5 years in a European vacation account if you deposit $200 a month in an account that is paying a nominal 12 percent per year, compounded monthly?

Accepted Answer

The answer of How much will you have at the...

Question 7

You purchased a piece of property for $30,000 nine years ago and sold it today for $83,190.What was your rate of return on your investment?

Accepted Answer

30,000 = 83,190(PVIFᵢ,₉)
.3606 = PVIFᵢ, ₉
From Table II, i = 12%
66.

Question 8

What is the most you should pay to receive the following cash flows if your required rate of return is 12 percent?
$\begin{array}{ll}
\text { Year } 1 & \$ 5,000 \
\text { Year } 2 & \$ 8,000 \
\text { Year } 3 & \$ 12,000 \
\text { Year 4-10 } & \$ 15,000
\end{array}$

Accepted Answer

PV = $5,000(0.893) + $8,000(0.797) + $12,000(0.712) + $15,000(5.650 - 2.402) = $68,105

Question 9

What is the present value of the following net cash flows if the discount rate is 12%:
$$\begin{array} { l l } 
\text { Year } & \text { Cash Flow } \
1 - 5 & \$ 10,000 \text { each year } \
6 - 10 & \$ 15,000 \text { each year } \
11 - 15 & \$ 17,000 \text { each year }
\end{array}$$

Accepted Answer

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

Question 10

Your local bank offers 4-year certificates of deposit (CD) at a 12 percent annual nominal interest rate compounded quarterly.Determine how much additional interest you will earn over 4 years on a $10,000 CD that is compounded quarterly compared with one that is compounded annually.

Accepted Answer

For a CD compounded quarterly, the effective annual interest rate is:

(1 + (0.12/4))^4 - 1 = 0.126825 or 12.6825%

For a CD compounded annually, the effective annual interest rate is simply 12%.

After 4 years, the interest earned on a $10,000 CD compounded quarterly is:

$10,000(1 + 0.126825/4)^(4*4) - $10,000 = $17,857.20 - $10,000 = $7,857.20

After 4 years, the interest earned on a $10,000 CD compounded annually is:

$10,000(1 + 0.12)^4 - $10,000 = $16,129.60 - $10,000 = $6,129.60

The additional interest earned on the quarterly compounded CD compared to the annually compounded CD is:

$7,857.20 - $6,129.60 = $1,727.60 or $1,728 rounded to the nearest dollar.

Therefore, the best choice is C, $310, which is not an option. The closest answer is D, $220, but that is incorrect.

Question 11

You just purchased a new $25,000 car and agreed to pay for the car in 50 monthly payments.If the monthly interest rate is 1 percent, what is your total financing cost?

Accepted Answer

PMT = $25,000/39.196 = $637.82 I = $637.82(50) - $25,000 = $6,891

Question 12

Five years after an accident, you received $100,000 to pay the medical expenses incurred at the time of the accident.What is the present value (at the time of the accident) of the payment? Assume interest rates are 9%.

Accepted Answer

PV = 100,000(.65) = $65,000

Question 13

A bank has agreed to loan you $10,000 at 11% for 5 years.You are required to make equal, annual, end-of-year payments that include both principal and interest on the outstanding balance.Determine the amount of these annual payments (to the nearest dollar).

Accepted Answer

PVANₒ = $10,000;n = 5;i = 11% PVANₒ = PMT(PVIFAᵢ,n )
$10,000 = PMT(PVIFA₀.₁₁,₅ ) = PMT(3.696) PMT = $2,706

Question 14

A zero coupon bond with a $1,000 par value (future value) is selling for $356 and matures in 12 years.What is the implied discount rate (yield to maturity)?

Accepted Answer

PVIF = $356/$1000 = 0.356;or 9% from Table II

Question 15

Sales for Triad Inc.have grown from $2 million to $8.092 million in 10 years.What is the implied growth rate of sales for Triad?

Accepted Answer

2 = 8.092(PVIFᵢ,₁₀)
.2472 = PVIFᵢ,₁₀ From Table II, i = 15%

Question 16

Your brother, who is 6 years old, just received a trust fund that will be worth $25,000 when he is 21 years old.If the fund earns 10 percent interest compounded annually, what is the value of the fund today?

Accepted Answer

PV = $25,000(0.239) = $5,975

Question 17

John borrowed $20,000 to finance his college education.If the finance charge on the loan is 6 percent, and he will pay off the loan in 10 equal, annual, end of year payments, how much total interest will he pay?

Accepted Answer

PMT = $20,000/7.360 = $2,717.39;Total payments = $27,173.90 I = $27,173.90 - $20,000 = $7,173.90

Question 18

If you invest the $10,000 you receive at graduation (age 22) in a mutual fund that averages a 12% annual return, how much will you have at retirement in 40 years?

Accepted Answer

FV = 10,000(93.051) = $930,510

Question 19

California Life has just offered you a single premium annuity for $5,000 that will pay $5,144.12 per year for 20 years, the first payment being received exactly 31 years from today.What is the implied rate of return on this annuity?

Accepted Answer

Trial and error, Try 8%
PVAN = $5,144.12(PVIFAᵢ,₂₀) = $5,144.12(9.818) = $50,505 PVAN(PVIFᵢ,₃₀) = $50,505(0.099) = $5,000

Question 20

Roy, who has just turned 40, would like to have an annual annuity of $20,000 paid over a 20 year period, the first payment occurring on his 66th birthday.How much must Roy save each year (end of year) for the next 25 years to have this annuity, if the investment will earn 12 percent compounded annually?

Accepted Answer

PVAN = $20,000(7.469) = $149,380 PMT = $149,380/133.334 = $1,120

Quiz 5: The Time Value of Money