Question

45 Points!!!!!!!!!!!!!!

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

Answer 1

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Explanation:

Answer 2

The equation for compound interest is:


`A = P(1+ (r)/(n))^( nt)`

Where r is the interest rate and n is the number of times per year it's applied.

Annually n = 1 and 7% interest r = 0.07
The quarterly rate 2% is already quartered 0.02 = r/n .


`(1+0.07)= (1+0.02 ) ^(4) \\ \\ 1.07 = (1.02) ^(4) \\ \\ 1.07 \\eq 1.082`

You can see that Alexander is incorrect. A quarterly compound interest rate of 2% will accrue more interest than a 7% compound annual interest rate.


`(1+0.07) = (1+ r) ^(4) \\ \\ 1.07 = (1+r) ^(4) \\ \\ \sqrt[4]{1.07} = r \\ \\ \sqrt[4]{1.07} - 1 = r \\ \\ r = 0.017`

1.7% compound quarterly