Question

1. Chris Spear invested $50,000 today in a fund that earns 8% compounded semiannually. To what amount will the investment grow in 3 years?

2. Sally Medavoy will invest $10,000 a year for 3 years in a fund that will earn 6% annual interest. If the first payment into the fund occurs today, what amount will be in the fund in 3 years?

3. John Fillmore's lifelong dream is to own his own fishing boat to use in his retirement. John has recently come into an inheritance of $500,000. He estimates that the boat he wants will cost $400,000 when he retires in 5 years. How much of his inheritance must he invest at an annual rate of 10% (compounded annually) to buy the boat at retirement?

4. Kehoe, Inc. owes $30,000 to Ritter Company today. How much would Kehoe have to pay each year if the debt is retired through four equal payments (made at the end of the year), given an interest rate on the debt of 12%?

5. On January 15, 2010, Dolan Corp. adopted a plan to accumulate funds for environmental improvements beginning July 1, 2014, at an estimated cost of $5,000,000. Dolan plans to make four equal annual deposits in a fund that will earn interest at 8% compounded annually. The first deposit was made on July 1, 2010. Dolan should make four annual deposits of ?

Answer 1

Answer to Question 1:

Amount Invested = $50,000

Annual Interest Rate = 8.00%
Semiannual Interest Rate = 4.00%

Time Period = 3 years
Semiannual Period = 6

Accumulated Sum = Amount Invested * (1 + Semiannual Interest Rate)^Semiannual Period
Accumulated Sum = $50,000 * 1.04^6
Accumulated Sum = $50,000 * 1.265319
Accumulated Sum = $63,265.95

Answer to Question 2:

Annual Deposit = $10,000
Time Period = 3 years
Interest Rate = 6%

Accumulated Sum = $10,000*1.06^3 + $10,000*1.06^2 + $10,000*1.06
Accumulated Sum = $10,000 * 1.06 * (1.06^3 - 1) / 0.06
Accumulated Sum = $10,000 * 3.374616
Accumulated Sum = $33,746.16