If $7,000 is invested at 7% interest for 20 years, there will be $400 more if the compounding is continuous rather than quarterly.

Question

Quizplus · Accepted Answer

Continuous compounding at a rate of 7% for 20 years yields $A = P e^{rt} = 7000e^{0.07 \times 20} \approx \$27,126.81$, while quarterly compounding yields $A = P \left(1 + \frac{r}{n}\right)^{nt} = 7000\left(1 + \frac{0.07}{4}\right)^{4 \times 20} \approx \$26,532.98$. The difference is approximately $593.83, not $400.

If $7,000 Is Invested at 7% Interest for 20 Years