Solve the problem.
-James wants to invest $8,000. He can invest the money at 7.2% simple interest for 30 yr or he can invest at 7% with interest compounded continuously for 30 yr. Which option results in more total
Interest?
A) 7% compounded continuously results in more total interest
B) 7.2% simple interest results in more total interest

Question

Quizplus · Accepted Answer

For simple interest, the formula is $A = P(1 + rt)$, where $A$ is the future value, $P$ is the principal amount, $r$ is the rate, and $t$ is the time in years. Plugging in the values for the 7.2% simple interest option: $A = 8000(1 + 0.072 \times 30) = 8000(1 + 2.16) = 8000 \times 3.16 = 25280$. The total interest earned is $25280 - 8000 = 17280$.For compound interest compounded continuously, the formula is $A = Pe^{rt}$, where $e$ is the base of the natural logarithm (approximately 2.71828). Plugging in the values for the 7% compounded continuously option: $A = 8000e^{0.07 \times 30} = 8000e^{2.1} \approx 8000 \times 8.166 = 65328$. The total interest earned is $65328 - 8000 = 57328$.Comparing the total interest earned from both options, the 7% compounded continuously yields more total interest.

Solve the Problem. -James Wants to Invest $8,000. He Can Invest the Money