Question

Rebecca deposited money into his retirement account that is compounded annually at an interest rate of 7%. Rebecca thought the equivalent quarterly interest rate would be 2%. Is Rebecca correct ? If she is, explain why. If she is not correct state what the equivalent quarterly interest rate is and show how you got your answer.

Answer 1

Rebecca is incorrect. The equivalent quarterly interest rate is 1.75%.

Step-by-step explanation:

The formula for compound interest is i = r/n.

r represents the interest rate in decimal form.

n represents the compounding periods in a year.

Calculate the interest rate for 7% compounded quarterly:

Since interest compounded quarterly is four times a year, n = 4.

7% is converted to decimal form by dividing by 100.

7 / 100 = 0.07

r = 0.07

Substitute these into the formula:

i = r/n

= 0.07/4

= 0.0175

0.0175 is in decimal form. To convert it to a percentage, multiply it by 100.

0.0175 X 100 = 1.75%

1.75% ≠ 2%

Therefore, Rebecca is incorrect. The equivalent quarterly interest rate is 1.75%.