Question

kirk van houten, who has been married for 22 years, would like to buy his wife an expensive diamond ring with a platinum setting on their 30 year wedding ring anniversary. Assume that the cost of the ring will be $9,166 in 8 years. kirk currently has $4,600 to invest. What annual rate of return must kirk earn on his investment to accumulate enough money to pay for the ring?

Answer 1

Formula for compound interest can be used to compute rate of investment as:

A = P x (1 + r/m) ^mt

r/m = [(A /P) ^1/mt ] – 1

A = Future value of investment = $ 9,166

P = Principal = $ 4,600

r = Rate of interest

m = No. of compounding in a year = 1 [assumed]

t = No. of years = 8

r = [($ 9,166 /$ 4,600) ^1/8] – 1

= [(1.99260869565217) ^1/8] – 1

= [(1.99260869565217)^0.125] – 1

= 1.09000314910495 – 1

  = 0.09000314910495 or 9 %

Kirk van should earn 9 % annual return to accumulate the required money.