The R&M Bank currently offers an investment account with an interest rate of 6% compounded monthly.R&M wants to offer customers another account with interest compounded quarterly.If R&M wants the effective rates to be equal, what interest rate should R&M quote for the second account?
A)2.00%
B)6.00%
C)6.03%
D)6.17%

Question

Quizplus · Accepted Answer

We can use the formula for effective annual interest rate to solve this problem. The formula is:

Effective annual interest rate = (1 + (nominal interest rate / n))^n - 1

where n is the number of times the interest is compounded in a year.

For the first account, n = 12 (compounded monthly) and the nominal interest rate is 6%. Plugging these values into the formula, we get:

Effective annual interest rate = (1 + (0.06 / 12))^12 - 1 ≈ 6.17%

For the second account, R&M wants the effective annual interest rate to be the same as the first account, which is approximately 6.17%. However, the interest is compounded quarterly, so we need to solve for the nominal interest rate. Plugging in n = 4 and the desired effective annual interest rate of 6.17%, we get:

6.17% = (1 + (r / 4))^4 - 1

Solving for r, we get r ≈ 6.03%. Therefore, R&M should quote an interest rate of 6.03% for the second account if they want the effective rates to be equal. Thus, the best choice is C.

The R&M Bank Currently Offers an Investment Account with an Interest