How much should she invest now at 6%, compounded quarterly, so that she will have enough to buy a new car

Question

Barbara knows that she will need to buy a new car in 4 years. The car will cost $15,000 by then. How much should she invest now at 6%, compounded quarterly, so that she will have enough to buy a new car

Answer 1

A = P(1 + r/n)^nt

 

Where:

P = the unknown initial investment

A = the final value = $15,000

r = the annual interest rate = 6% = 0.06

n = the number of times the investment is compounded per year = quarterly = 4

t = years = 4

 

$15000 = P(1 + 0.06/4)^4*4

 

$15000 = P(1.015)¹⁶

 

$15000 = P*(1.269)

 

$15000/(1.269) = P

 

Solve for P