Question

1. Alberto purchased a diamond ring for his girlfriend today. He will pay $320 (interest and principal) at the end of each year for the next 8 years. Assuming that the store is charging Alberto 6% interest, what was the purchase price of the gift? (Round your answer to the nearest dollar)

2.Georgia deposited money in her retirement account 11 years ago. Today her account has $8600 in it. Assuming a 4% interest rate. how much did Georgia deposit 11 years ago? (Round your answer to the nearest dollar)

3.Three years ago, Nina borrowed $13600 from me. Today, she will repay the loan, along with interest at 8%. How much am I going to receive? (Round your answer to the nearest dollar)

Answer 1

1. Purchase price of gift shall be present value of cash outflow from Alberto.

Installment = $ 320 at end of each year for 8 year

Interest = 6%

Present value = 320 PVIFA (6%,8) i.e. present value of $320 paid each year for 8 year discounted at 6%

= 320 * Present value annuity factor for 8 year @ 6%.

= 320 * 6.2098

= $ 1,987

Purchase price of gift = $ 1,987

2. The deposited money by Georgia shall be the present value of $ 8,600, 11 years ago discounted @ 4%

Deposited money = 8,600 PVAFA (4%,11)

= 8,600 * Present value factor for 11 year @ 4%

= 8,600 * 0.6496

= $ 5,586.40

3. The received amount today shall be the Principal + Interest.

Interest shall be assumed to be compounding per year.

Received amount = $ 13,600 *1.08 *1.08*1.08

= $ 17,132