Question

Answer questions A- J:

Question A

You have $2,000 to invest and hope to eventually have $10,000. What interest rate must you earn in order to reach your goal in 25 years?

Question B

You have just invested in a bank account that earns 2% per year. How long will it take to double your money?

Question C  

A gallon of gas costs $3.00 in 2018. If inflation will be 3.5%, assuming the price of gasoline only increases with inflation, how much a gallon of gas cost in 40 years?

Question D

Compounding is:

	A) The process of computing the future value from the number of time periods.
	B) The process of computing the present value from the future value.
	C) The process of computing the future value from the present value.
	D) The process of computing the amount of interest from the present value.

Question E

Time Value of Money concepts are based on the idea that a dollar today is worth less than a dollar in the future.

True

False

Question F

You win the lottery! You can either take the money now or wait 25 years and receive it then. If you get it now, then the best investment that you found is a 25 year CD that will earn 4%/year. The lottery offers you $5,000,000 if take the winnings today or $15,000,000 if you wait 25 years. Assuming their are no other risks, taxes, or opportunity costs (i.e. missing out on the fun of having $5 million now is not a deciding factor), what should you do?

	A) Take the $5,000,000 now and invest it in the CD
	B) Take the $15,000,000 in 25 years

Question G

Holding present value and discount rate constant, the greater the number of periods...

	A) the lower the future value.
	B) the greater the future value.
	C) has no impact on future value.

Question H

Holding future value and discount rate constant, the greater the number of periods...

	A) the lower the present value.
	B) the greater the present value.
	C) has no impact on present value.

Question I

When Amy was four years old, she received $500 from her relatives as a birthday gift. Her mom helped her deposit the money in a bank account. The interest rate on the account has been fixed at 5% compounded monthly. Now Amy is 16 years old. How much does she have on the account?

Question J

Jean’s daughter is a freshman at a university. She plans to study abroad during her last semester at the university. The abroad program will cost her $5000. Jean wants to pay for the program. How much money does Jean have to set aside today in order to pay for the program three and a half years from now? The money will be invested in a CD which pays 6% interest rate compounded annually.

Answer 1

QUESTION A

This question requires application of basic time value of money function, FV = PV * (1 + r)ⁿ

For our question, FV = $10000, PV = $2500, n = 25, r=?

10000 = 2500 * (1 + r)²⁵

(1 + r)²⁵ = 4

1 + r = 1.0570

r = 5.70% --> Answer

QUESTION B

Again using the same TVM function,

FV = 2PV, r = 2%, n =?

2PV = PV * (1 + 2%)ⁿ

2 = (1.02)ⁿ

Taking natural log on both sides

LN (2) =n * LN(1.02)

n = 35 years --> Answer

QUESTION C

Again using the same TVM function,

FV = ? PV = 3, r = 3.5%, n =40years

FV = 3 * (1 + 3.5%)⁴⁰

FV = $11.88 --> Answer

QUESTION D

Compounding is The process of computing the future value from the present value. Hence Answer is Option C. The reverse process,of computing present value from future value is termed as Discounting.

QUESTION E

Statement is FALSE. Time Value of Money concepts are based on the idea that a dollar today is worth MORE than a dollar in the future. This is because the money earned today has a power of compounding. In simple words, if I give you a a dollar today, you would be able to earn some interest on that (from bank), so if you were to earn 10% interest, it would have grown to $1.1 in 1 year. This would have been higher than $1, that I would have given you next year.

QUESTION F

We first need to compute the FV of $5 mil, if that was invested for 25 years in CD offering 4% return.

FV = 5,000,000 * (1 + 4%)²⁵

FV = 13,329,181.66

This FV is less than the amount offered by the company in 25 years which is $15,000,000. Hence take $15,000,000 after 15 years should be the best decision. Option B --> Answer

QUESTION G

Answer this question using the TVM function we used earlier:

FV = PV * (1 + r)ⁿ

Until the rates are positive, FV is directly proportional to the number of periods, i.e., more than the number of periods greater would the value of FV be. Hence, Option B is answer.

QUESTION H

Answer this question using the TVM function we used earlier:

FV = PV * (1 + r)ⁿ

This implies, PV = FV/(1 + r)ⁿ

Here, the PV has an inverse relation with number of periods, i.e., as the number of periods increase, PV decreases. Hence, Option A is answer.

QUESTION I

PV = $500, r = 5% per year --> 5%/12 per month = 0.4167% per month, n = 12 years --> 144 months

FV = 500 * (1 + 0.004167)¹⁴⁴

FV = $909.92 --> Answer

QUESTION J

Again using the same TVM function,

5000 = PV * (1 + 6%)^3.5

PV = $4077.55 --> Answer