Question 1

A one-time gift to your college will provide $25,000 in scholarship funds next year with that amount increasing by 2 percent annually thereafter. If the discount rate is 5.5 percent, what is the current value of this perpetual gift?

Accepted Answer

The current value of a perpetual gift that grows at a rate different from the discount rate can be calculated using the formula: $PV = \frac{C}{r - g}$, where $PV$ is the present value, $C$ is the initial cash flow, $r$ is the discount rate, and $g$ is the growth rate. Here, $C = \$25,000$, $r = 5.5\% = 0.055$, and $g = 2\% = 0.02$. Plugging these values into the formula gives: $PV = \frac{\$25,000}{0.055 - 0.02} = \frac{\$25,000}{0.035} = \$714,285.71$.

Question 2

Sara wants to establish a trust fund to provide $75,000 in scholarships each year and earn a fixed 6.15 percent rate of return. How much money must she contribute to the fund assuming that only the interest income is distributed?

Accepted Answer

The answer of Sara wants to establish a trust fund...

Question 3

You want to buy a new sports car for $55,000. The contract is in the form of a 60-month annuity due at an APR of 5.6 percent, compounded monthly. What will be your monthly payment?

Accepted Answer

To calculate the monthly payment of the annuity due, we can use the formula:
P = A/(1 - (1+r/n)^(-nt)), where P is the monthly payment, A is the amount borrowed, r is the annual interest rate, n is the number of times in a year that interest is compounded, and t is the number of years.
Plugging in the values, we get:
P = 55000/(1 - (1+0.056/12)^(-60*12/12))
P = $1,048.21
Therefore, the monthly payment will be $1,048.21, which is closest to choice C.

Question 4

You just won the magazine sweepstakes and opted to take unending payments. The first payment will be $50,000 and will be paid one year from today. Every year thereafter, the payments will increase by 2.5 percent annually. What is the present value of your prize at a discount rate of 7.9 percent?

Accepted Answer

The answer of You just won the magazine sweepstakes and...

Question 5

You grandfather invested $16,600 years ago to provide annual payments of $700 a year to his heirs forever. What is the rate of return?

Accepted Answer

To find the rate of return, we can use the formula for perpetuity payments:

(rate of return) = (annual payment) / (original investment)

Plugging in the values from the problem, we get:

(rate of return) = 700 / 16,600

(rate of return) ≈ 0.0422, or 4.22%

Therefore, the rate of return is 4.22%, which corresponds to choice B.

Question 6

You just settled an insurance claim that calls for increasing payments over a 10-year period. The first payment will be paid one year from now in the amount of $5,000. The following payments will increase by 3.5 percent annually. What is the value of this settlement to you today if you can earn 6.5 percent on your investments?

Accepted Answer

The answer of You just settled an insurance claim that...

Question 7

Beginning three months from now, you will need $1,500 each quarter for the next four years to cover expenses. How much do you need to have saved today to meet these needs if you can earn .35 percent interest per quarter?

Accepted Answer

The correct answer is A because $23,300.75 is the amount that needs to be saved today to meet the expenses.

Question 8

Your grandfather left you an inheritance that will provide an annual income for the next 20 years. You will receive the first payment one year from now in the amount of $2,500. Every year after that, the payment amount will increase by 5 percent. What is your inheritance worth to you today if you can earn 7.5 percent on your investments?

Accepted Answer

To find the present value of the inheritance, we need to discount the future cash flows back to present using the given discount rate of 7.5%.

We can use the formula for the present value of an annuity with growth:

PV = C / (r-g) * (1 - (1+g)/(1+r)^n)

where 
C = first payment = $2,500 
r = discount rate = 7.5% or 0.075 
g = growth rate = 5% or 0.05 
n = number of years = 20

Plugging in the values, we get:

PV = 2500 / (0.075 - 0.05) * (1 - (1+0.05)/(1+0.075)^20) 
PV = $37,537.88

Therefore, choice A is the correct answer as it represents the present value of the inheritance.

Question 9

Today, you turn 21. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $75 a day, every day, until you turn 40. You open an investment account and deposit your first $75 today. What rate of return must you earn to achieve your goal? Note: Ignore Leap Years.

Accepted Answer

The answer of Today, you turn 21. Your birthday wish...

Question 10

You just paid $480,000 for an annuity that will pay you and your heirs $15,000 a year forever. What rate of return are you earning on this policy?

Accepted Answer

The rate of return on a perpetuity is calculated by dividing the annual payment by the purchase price. Here, $15,000 / $480,000 = 0.03125, or 3.125 percent.

Question 11

You just received an offer in the mail to transfer the $5,000 balance from your current credit card, which charges an annual rate of 18.7 percent, to a new credit card charging a rate of 7.9 percent. You plan to make payments of $250 a month on this debt. How many fewer payments will you have to make to pay off this debt if you transfer the balance to the new card?

Accepted Answer

The answer of You just received an offer in the...

Question 12

Western Bank offers you a $12,000, 6-year term loan at 7 percent annual interest. What is the amount of your annual loan payment?

Accepted Answer

The annual loan payment can be calculated using the formula for an annuity payment: P = [r*PV] / [1 - (1 + r)^-n], where P is the payment, r is the interest rate per period, PV is the present value (loan amount), and n is the number of periods. For this loan, r = 0.07, PV = $12,000, and n = 6. Plugging these values into the formula gives an annual payment of approximately $2,517.55.

Question 13

A preferred stock pays an annual dividend of $5.20. What is one share of this stock worth today if the rate of return is 10.44 percent?

Accepted Answer

To determine the current value of the preferred stock, we can use the dividend discount model:

PV = D / r

where PV is the present value, D is the annual dividend, and r is the required rate of return.

Plugging in the given values, we get:

PV = 5.20 / 0.1044 = $49.81

Therefore, one share of this stock is worth $49.81 today. The correct answer is (C).

Question 14

Your father helped you start saving $25 a month beginning on your fifth birthday. He always made you deposit the money into your savings account on the first day of each month just to "start the month out right." Today completes your 15th year of saving and you now have $6,528.91 in this account. What is the rate of return on your savings?

Accepted Answer

The rate of return can be calculated using the formula for the future value of a series: FV = P * [(1 + r)^n - 1] / r, where FV is the future value of the savings, P is the payment amount per period, r is the rate of return per period, and n is the total number of payments. Given that the savings amount is $6,528.91, the monthly deposit is $25, and the total number of deposits over 15 years (180 months) is known, we can solve for r (the monthly rate of return) and then annualize it. The correct rate of return that matches the given future value under these conditions is approximately 4.67 percent annually.

Question 15

What is the present value of $1,400 a year at a discount rate of 8 percent if the first payment is received 7 years from now and you receive a total of 25 annual payments?

Accepted Answer

The present value of an annuity can be calculated using the formula PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the annual payment, r is the discount rate per period, and n is the total number of payments. However, since the first payment is received 7 years from now, we need to discount the calculated present value of the annuity back 6 years (to account for the payment starting in year 7). The correct present value, given the options, is $9,417.69, which accounts for both the calculation of the annuity's present value and the additional step of discounting that value to the present considering the delay in the start of the payments.

Question 16

Your credit card company charges you 1.15 percent interest per month. What is the APR?

Accepted Answer

The answer of Your credit card company charges you 1.15...

Question 17

For the next 20 years, you plan to invest $600 a month in a stock account earning 7 percent and $400 a month in a bond account earning 4 percent. When you retire in 20 years, you will combine your money into an account with a return of 5 percent. How much can you withdraw each month during retirement assuming a 30-year withdrawal period?

Accepted Answer

The answer of For the next 20 years, you plan...

Question 18

DLM preferred stock has a dividend yield of 5.2 percent. The stock is currently priced at $43.40 per share. What is the amount of the annual dividend?

Accepted Answer

The answer of DLM preferred stock has a dividend yield...

Question 19

You would like to provide $125,000 a year forever for your heirs. How much money must you deposit today to fund this goal if you can earn a guaranteed 4.5 percent rate of return?

Accepted Answer

To find the amount needed to deposit today to provide $125,000 a year forever at a 4.5% rate of return, you use the formula for a perpetuity: Present Value = Payment / Interest Rate. Plugging in the numbers: $125,000 / 0.045 = $2,777,778.

Question 20

Jones Stoneware has a liability of $75,000 due four years from today. The company is planning to make an initial deposit today into a savings account and then deposit an additional $10,000 at the end of each of the next four years. The account pays interest of 4.5 percent. How much does the firm need to deposit today for its savings to be sufficient to pay this debt?

Accepted Answer

The answer of Jones Stoneware has a liability of $75,000...

Quiz 6: Discounted Cash Flow Valuation