Compounding interest is driving me crazy!! Please help!

imdoinmenow

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May 25, 2012
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Customer deposited $15,000 in a new savings account at 9% interest compounded semiannually. At the beginning of year 4, he deposits an additional $40,000 at 9% interest compounded semiannually. What is the balance of the account at the end of 6 years?

This is what I did: 9%/2= 4.5
Then I took the $15,000 * 4.5%=675
Added that amount to the beginning balance 15,000+675=15675 at end of year one

15,675*4.5%=705.38 +15,675=16,380.38 year two

16,380.38*4.5%=737.12+16380.38=17117.50 year three

17,117.50*4.5%=770.29+17,177.50=17,887.79 year four

17,887.79 + 40,000 (additional deposit)=57,887.79 * 9% semiannually

57,887.79 *4.5= 2604.95 + 57,887.79=60,492.74 year five

60,492.74 * 4.5=2722.17 +60, 492.74=63,214.91 year six

Please tell me I'm right...


 
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