Problem – Pre-Calculus – How to Calculate Compound Interest on an Investment

In this problem, we walk through a question on calculating compound interest. In the explanation video, we spend some time on on the compound interest formula, itself, and distinguish it from simple interest scenarios.

**Comparison with Simple Interest: **Notice that at the end of the investment period, you can see the impact of compounding. For example, in Part (a) of this problem, simple interest would yield $1,060.00 whereas we calculated that compounding yields $1,061.36 — or a difference of $1.36 due to the compounding. While this isn’t very much difference in just one year, the difference grows when the compounding is allowed time to grow. In part (b), simple interest in two years yields $1,120.00 compared to $1,126.49 (a difference of $6.49). Part (c), in 5 years, simple interest yields $1,300.00 versus $1,346.86 (a difference of $46.86). And in Part (d), a simple interest investment would yield $1,600.00 after 10 years compared to $1,814.02 with compounding (a difference of $214.02) — significantly more growth than in the simple interest scenario. In fact, you would need a simple interest rate of 8.14% to match the compound growth at 6% in 10 years!