The Effective Interest Rate Calculation for Savings and Loan

How to calculate the effective interest rate for a savings and loan that pays 6% interest compounded monthly?

A. 6.08%

B. 6.52%

C. 6.17%

D. 6.81%

Answer:

The effective interest rate on a loan that pays 6% compounded monthly over the course of a year is 6.17%.

The effective interest rate is a crucial metric in finance that represents the true cost of borrowing or the true return on investment. In this case, we are tasked with finding the effective interest rate for a savings and loan plan that offers 6% interest compounded monthly.

To calculate the effective rate of interest for this scenario, we use the formula (1 + i/n)^(n*t) - 1, where i is the nominal rate, n is the number of compounding periods in a year, and t is the time in years.

Plugging in the values for i = 6% = 0.06, n = 12 (compounded monthly), and t = 1 year, we get:

((1 + 0.06 / 12)^(12 * 1)) - 1 = 0.0616778118645

Converting this decimal to a percentage, we find that the effective rate of interest is 6.17%, which corresponds to answer option C.

In conclusion, when a savings and loan pays 6% interest compounded monthly, the effective interest rate is 6.17%, indicating the true cost of borrowing for this financial product.