A newborn child receives a ​$5,000 gift toward a college education from her grandparents. How much will the $5,000 be worth in 19 years if it is invested at 5.3​% compounded​ quarterly?

Question

A newborn child receives a ​$5,000 gift toward a college education from her grandparents. How much will the $5,000 be worth in 19 years if it is invested at 5.3​% compounded​ quarterly?

Answer 1

Compound interest is modeled by the equation:

A(t) = A₀(1 + r/n)^nt where A(t) is the amount at any time "t", A₀ is the initial amount (the amount at "t = 0"), "r" is the interest rate (usually annual), "n" is the number of compounding periods (for quarterly, "n = 4"), and "t" is the time (usually years).

So, A(19) = 5000(1 + 0.053/4)^4•19

A(19) = 5000(1.01325)⁷⁶

A(19) = 5000•2.719333942

A(19) = $13596.67