Question

Bill O’Brien would like to take his wife, Mary, on a trip three years from now to Europe to celebrate their 40th anniversary. He has just received a $26,000 inheritance from an uncle and intends to invest it for the trip. Bill estimates the trip will cost $30,000 and he believes he can earn 4% interest, compounded annually, on his investment. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1).

What interest rate, compounded annually, must Bill earn to accumulate enough to pay for the trip?

Answer 1

Bill must earn at 4.89% interest rate

Step-by-step explanation:

The rate that Bill must earn on the $26,000 in order to be able to accumulate $30,000 in three years' time is computed below using the future value formula:

FV=PV*(1+r)^N

FV is the future value of $30,000

PV is the principal to be invested today of $26,000

N is the duration of the investment of 3 years

r is the unknown

30,000=26000*(1+r)^3

divide both sides by 26,000

30000/26000=(1+r)^3

divide the index on both sides by 3

(30000/26000)^(1/3)=1+r

r=(30000/26000)^(1/3)-1

r=1.048856246 -1

r=0.048856246

r=4.89%