Question

 Matt Johnson delivers newspapers and is putting away ​$30 at the end of each quarter from his paper route collections. Matt is 13 years old and will use the money when he goes to college in 5 years. What will be the value of​ Matt's account in 5 years with his quarterly payments if he is earning 7​% ​(APR), 8 % ​(APR), or 13.5 % ​(APR)?

Answer 1

Amount Deposited at the end of each quarter = P = $30

Number of Years to start college = 5 years

Number of quarters to start college = n = 5*4 = 20 quarters

If Interest Rate earned = r = 7% per year = 0.07/4 quarterly

Future Value of Investment = P(1+r)^n-1 +....+ P(1+r)² + P(1+r) + P = P[(1+r)ⁿ -1]/r = 30[(1+0.07/4)²⁰ -1]/(0.07/4) = $711.05

If Interest Rate r = 8% APR = 0.08/4,

Future Value of Investment = P[(1+r)ⁿ -1]/r = 30[(1+0.08/4)²⁰ -1]/(0.08/4) = $728.92

If Interest Rate r = 13.5% APR = 0.135/4,

Future Value of Investment = P[(1+r)ⁿ -1]/r = 30[(1+0.135/4)²⁰ -1]/(0.135/4) = $837.58