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Math Help - check my answer

  1. #1
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    check my answer

    Find the accumulated value of 2480 at the end of twelve years, if the nominal interest rate was 2% convertible monthly for the first three years, the nominal rate of discount was 3% convertible semi-annually for the next two years, the nominal rate of interest was 4.2% convertible once every two years for the next four years, and the annual effective rate of discount was 5.8% for the last three years.

    i did:

    [2480(1+0.02/12)^36][1-0.03/2]^-4[1+0.042]^2[1-0.058]^-3= 3633.50

    im am not sure if i got the right answer, could anyone please check and explain my mistake to me if i have one. thank you.
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  2. #2
    Member jonah's Avatar
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    <br />
2,480\left( {1 + \frac{{.02}}<br />
{{12}}} \right)^{3 \times 12} \left( {1 + \frac{{.03}}<br />
{2}} \right)^{2 \times 2} \left( {1 + \frac{{.042}}<br />
{{\tfrac{1}<br />
{2}}}} \right)^{4 \times \tfrac{1}<br />
{2}} \left( {1 + \frac{{.058}}<br />
{1}} \right)^{3 \times 1}  \approx 3,889.263749<br />
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  3. #3
    MHF Contributor
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    Hold on there, Jonah. Interest is NOT the same as Discount.

    1) Both managed the first factor.
    2) Only mathlovet managed the second and fourth factors.
    3) Only jonah managed that nasty third factor.

    Kind of a mixed bag.

    All told, we should get $3,932.32
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  4. #4
    Member jonah's Avatar
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    Quote Originally Posted by mathlovet View Post
    Find the accumulated value of 2480 at the end of twelve years, if the nominal interest rate was 2% convertible monthly for the first three years, the nominal rate of discount was 3% convertible semi-annually for the next two years, the nominal rate of interest was 4.2% convertible once every two years for the next four years, and the annual effective rate of discount was 5.8% for the last three years.

    i did:

    [2480(1+0.02/12)^36][1-0.03/2]^-4[1+0.042]^2[1-0.058]^-3= 3633.50

    im am not sure if i got the right answer, could anyone please check and explain my mistake to me if i have one. thank you.
    I confess I did not notice those two. I dismissed the problem as another ordinary compound interest situation. I seem to have gotten into a bad habit of not paying close attention to details lately. It's a good thing TKHunny noticed my carelessness.
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