Maria plans to use $18,000 to open a savings account with an annual interest rate of 7%. How much more interest will she earn over 6 years if she chooses an account that compounds interest quarterly instead of annually? interest compounded quarterly: A = P (1 + )4t interest compounded annually: A = P (1 + r)t $

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01-06-2016
Mathematics

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Maria plans to use $18,000 to open a savings account with an annual interest rate of 7%. How much more interest will she earn over 6 years if she chooses an account that compounds interest quarterly instead of annually? interest compounded quarterly: A = P (1 + )4t interest compounded annually: A = P (1 + r)t $

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Hagrid Hagrid · Answer 1 · 2016-06-14T17:56:47+02:00

Judging from the formulas given, I assume that the interest rate for the second account is 7% per quarter.

If he account is compounded 7% annually, the value of the account after 6 years is A=18000(1+0.07)^6=$27,013.15.

If the account is compounded 7% quarterly, the value of the account after 6 years (or 24 quarters) is A=18000(1+0.07)^(6*4)=$91,302.61.

The difference in interest gained is also the difference in the final values of both accounts: $91,302.61-$27,013.15=$64,289.46.

However, if what you mean is 7% PER YEAR compounded QUARTERLY, this is a different story. This is the same as compounding at 7%/4=1.75% every quarter.