Question

Molly Hamilton deposited $50,000 at Bank of America at 8% interest compounded quarterly. What is the effective rate (APY) to the nearest hundredth percent?

Answer 1

The effective rate, or APY, for a $50,000 deposit at 8% interest compounded quarterly is approximately 8.24%.

Step-by-step explanation:

To find the effective rate (APY) compounded quarterly, we can use the formula:

APY = (1 + (interest rate / number of compounding periods))^number of compounding periods - 1

Substituting the given values, we get:

APY = (1 + (0.08 / 4))^4 - 1

APY = (1.02)^4 - 1

APY = 1.0824 - 1

APY ≈ 0.0824 or 8.24%

Answer 2

To find the effective rate (APY) of a deposit at Bank of America with a principal of $50,000 and an 8% interest rate compounded quarterly, use the formula APY = (1 + rac{r}{n})ⁿ - 1. Plugging in the values, the APY is approximately 8.24%.

Step-by-step explanation:

To find the effective rate (APY), we can use the formula:

APY = (1 + rac{r}{n})ⁿ- 1

where r is the annual interest rate and n is the number of compounding periods in a year.

In this case, the principal amount is $50,000 and the interest rate is 8% (or 0.08). Since interest is compounded quarterly, n = 4. Plugging these values into the formula, we get:

APY = (1 + rac{0.08}{4})⁴ - 1 = (1 + 0.02)⁴⁻¹

Calculating this expression, we find the effective rate (APY) to the nearest hundredth percent is approximately 8.24%.