11th edition, PS #75

by **guest 09.11** Tue Sep 11, 2007 11:36 am

The book's explanation uses the interest formula. How would one approach this problem w/o using the interest formula?

Leona bought a 1 year $10,000 certficate of deposit that paid interest at an annual rate of 8% compounded annually. What was the total amount of interest paid on this certificate at maturity?

$10,464
$864
$816
$800
$480

by **StaceyKoprince** Thu Sep 13, 2007 5:42 pm

They ask for the interest only, and it's only being earned for 1 year, so I know the answer is not going to be A. Cross it off.

8% compounded annually for one year is just 8% of your starting number. Are you sure that's the correct wording of this problem?

by **guest** Fri Sep 14, 2007 10:51 am

Hi Stacey,
Thanks for responding. Yes this is the entire problem.

by **guest** Fri Sep 14, 2007 10:55 am

Oops..one thing, its compounded semi-annually.

Does that mean you divide the 8% by 2? So, you get 4%. Then you multiply this by the principal, $10,000?

by **StaceyKoprince** Mon Sep 17, 2007 9:29 pm

Okay, semi-annually makes a lot more sense.

That means you have to do the entire calculation twice, because the second time it compounds you must base the calculation on the new principal amount, which includes what was earned in the first half of the cycle.

So after 6 months, she earns 4% of $10,000, which equals 400. The new principal amount is $10,000 + $400 = $10,400.

After another 6 months, she earns 4% NOT of $10,000 but of $10,400. This equals $416. The final amount is $10,400 + $416 = $10,816.

The interest is $10,816 - $10,000 = $816.