Consider a deposit of $100,000 that can be made into one of four banks. Which of the following provides the largest balance by the end of five years?
A) Bank A: 4.7% compounded continuously
B) Bank B: 4.8% compounded monthly
C) Bank C: 5% compounded annually
D) Bank D: 5.1% simple interest

Question

Quizplus · Accepted Answer

To find the largest balance after five years, we calculate the future value for each option. For continuous compounding, the formula is $A = P e^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate, $t$ is the time in years, and $e$ is the base of the natural logarithm (approximately 2.71828). For monthly compounding, the formula is $A = P(1 + \frac{r}{n})^{nt}$, where $n$ is the number of times the interest is compounded per year. For annual compounding, the formula simplifies to $A = P(1 + r)^t$. For simple interest, the formula is $A = P(1 + rt)$.A) For Bank A with 4.7% compounded continuously: $A = 100,000e^{0.047 \times 5} \approx 100,000 \times e^{0.235} \approx 100,000 \times 1.2649 = 126,490$B) For Bank B with 4.8% compounded monthly: $A = 100,000(1 + \frac{0.048}{12})^{12 \times 5} \approx 100,000(1 + 0.004)^{60} \approx 100,000 \times 1.2697 = 126,970$C) For Bank C with 5% compounded annually: $A = 100,000(1 + 0.05)^5 = 100,000 \times 1.2763 = 127,630$D) For Bank D with 5.1% simple interest: $A = 100,000(1 + 0.051 \times 5) = 100,000 \times 1.255 = 125,500$Bank C provides the largest balance after five years.

Consider a Deposit of $100,000 That Can Be Made into One