Question 1

Mark Larken promised his grandson Ralph that he would give him $3,000 six years from today for graduating from high school. If money is worth 10% compounded semiannually, what is the present value of this money?

Accepted Answer

10% / 2 = 5%, 6 × 2 = 12 periods, $3,000 × .5568 = $1,670.40.

Question 2

Marcia Gadzera wants to retire in San Diego when she is 65 years old. Marcia is now 50 and believes she will need $900,000 to retire comfortably. To date, she has set aside no retirement money. If she gets interest of 10% compounded semiannually, how much must she invest today to meet her goal of $900,000?

Accepted Answer

$900,000 × .2314 = $208,260.

Question 3

Travis Brown deposited $17,500 into Browning Bank, which pays 4% compounded quarterly. Calculate how much Travis will have in his account at the end of seven years.

Accepted Answer

4% / 4 = 1%, 7 × 4 = 28, $17,500 × 1.3213 = $23,122.75

Question 4

Helga Thalhimer will need to replace the registration software for her agency in five years. She received an estimate that it will cost $40,000 when she is ready to replace. What must Helga deposit today at 6% compounded quarterly to have enough to update her system?

Accepted Answer

6% / 4 = 1/5%, 5 × 4 = 20, $40,000 × .7425 = $29,700

Question 5

Abe Frill wants to attend AVP Tech. He will need to have $15,000 seven years from today. How much should Abe put in the bank today (12% quarterly)to reach his goal in the future?

Accepted Answer

12% / 4 = 3%, 7 × 4 = 28, $15,000 × .4371 = $6,556.50.

Question 6

Ryan deposits $12,000 into a fixed asset account that earns 6% compounded quarterly. What is Ryan's balance at the end of five years?

Accepted Answer

6% / 4 = 1.5%, 5 × 4 = 20 periods, $12,000 × 1.3469 = $16,162.80

Question 7

Al Safe deposited $15,000 at Q Bank at an interest rate of 16%, compounded quarterly. What was the effective rate (APY)? (round to nearest hundredth)

Accepted Answer

16% / 4 = 4%, 4 periods; 1.1699 × $15,000 = 17,548.50; $17,548.50 - $15,000.00 = $2,548.50; $2,548.50/$15,000.00 = 16.99%.

Question 8

Kelly Kuhn wants to purchase a new car for her son in five years. She estimates that the truck will cost $30,000 after all rebates. Assuming she invests at 8% compounded semiannually for five years, what must she invest today?

Accepted Answer

8% / 2 = 4%, 5 × 2 = 10, $30,000 × .6756 = $20,268

Question 9

Jim Ring wants to attend Northeast College. He will need $20,000 four years from today. If Jim's bank pays 8% compounded quarterly, what must he deposit today so that he will have the $20,000 in the future? Check your answer by use of the compound table value.

Accepted Answer

$20,000 × .7284 = $14,568; $14,568 × 1.3728 = $19,998.95 due to rounding of the table value

Question 10

Al Derover wants to buy a used jeep in five years. He estimates the cost will be $13,000. If he invests $8,500 now at a rate of 10% compounded semiannually, will he have enough money to buy the jeep at the end of five years? Show your work.

Accepted Answer

10% / 2 = 5%, 5 × 2 = 10 periods, $8,500 × 1.6289 = $13,845.65; yes.

Question 11

Jackie wants to purchase a lakeside condo in Cuba, Missouri, in 20 years. Jackie will invest in a mutual fund earning 8% compounded semiannually. How much will she need to deposit today in that fund to purchase her $100,000 lakeside condo?

Accepted Answer

8% / 2 = 4%, 20 × 2 = 40, $100,000 × .2083 = $20,830

Question 12

Mel Ross thinks he would like to buy a used car in five years for $8,000. He wants to put the money aside now so that in five years the $8,000 will be available. His bank offers him 12% interest, compounded semiannually. Could you calculate what Mel must invest today?

Accepted Answer

$8,000 × .5584 = $4,467.20.

Quiz 12: Compound Interest and Present Value