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.

Question

Mathematics

Adriel Waller

14 January, 08:44

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.

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Answers (1)

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Lorelai Robles · Answer 1

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

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%.