Question

James wants to invest $12,000. He can invest the money at 7.2% simple interest for 30 yr or he can invest at 6.8% with interest compounded continuously for 30 yr. Which option results in more total interest?

7.2% simple interest results in more total interest
6.8% compounded continuously results in more total interest

Answer 1

Over time, compound interest at any rate will outperform simple interest. When the rates are nearly equal to start with, compound interest will be greater in very short order. Here, it takes less than 1 year for compound interest to give a larger account balance.

In 30 years, the simple interest will be

... I = P·r·t = 12,000·0.07·30 = 25,200

In 30 years, the compound interest will be

... I = P·(e^(rt) -1) = 12,000·(e^(.068·30) -1) ≈ 80,287.31

_____

6.8% compounded continuously results in more total interest