Harry decided he was tired of being a poor college student when he visited a local electronics store and experienced its finest home theatre system.He determined that he would invest today a portion of the remaining money he earned last summer cleaning animal cages at the veterinary clinic.He plans to invest the money into an international mutual fund for 3.5 years and expects to earn an average annual rate of return of 15%.If Harry wants to have $4,000 in the account at the end of this time,how much must he invest today?
A)$1,253
B)$2,048
C)$2,453
D)$2,591

Question

Quizplus · Accepted Answer

We can use the formula for the future value of an annuity to solve this problem:

FV = PV(1+r)^n - PMT((1+r)^n-1)/r

Where:
FV = future value
PV = present value (amount to be invested today)
r = annual interest rate
n = number of periods (in years)

Substituting the given values:
FV = $4,000
r = 15% = 0.15
n = 3.5 years
PMT = 0 (there are no regular payments into the account, just a single lump sum investment)

$4,000 = PV(1+0.15)^3.5
$4,000 = PV(1.736)
PV = $2,306.42

Therefore, Harry must invest $2,306.42 today to have $4,000 in the account after 3.5 years. The closest answer choice to this value is C) $2,453.

Harry Decided He Was Tired of Being a Poor College