Question

Sam can invest $10,000 at either 4.75% compounded daily for 4 years or 5% compounded quarterly for 4 years. Which investment option will yield higher returns?

1) Investing at 4.75% compounded daily
2) Investing at 5% compounded quarterly
3) Both options will yield the same returns
4) Cannot be determined

Answer 1

Investing at 4.75% compounded daily will yield higher returns. The correct option is 1)

Step-by-step explanation:

When comparing two investment options, we need to consider the interest rate and the compounding frequency. The first option is an interest rate of 4.75% compounded daily for 4 years, while the second option is an interest rate of 5% compounded quarterly for 4 years. To determine which option will yield higher returns, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial investment), r is the annual interest rate, n is the compounding frequency, and t is the time in years.

For the first option, we have P = $10,000, r = 4.75%, n = 365 (daily compounding), and t = 4. Plugging in these values, we get A1 = 10000(1 + 0.0475/365)^(365*4). For the second option, we have P = $10,000, r = 5%, n = 4 (quarterly compounding), and t = 4. Plugging in these values, we get A2 = 10000(1 + 0.05/4)^(4*4).

By calculating the values of A1 and A2, we find that A1 ≈ $12,306.51 and A2 ≈ $12,167.77. Therefore, investing at 4.75% compounded daily will yield higher returns.