# Can somebody help..need to compare results as I think the book's wrong!

• Feb 26th 2010, 07:38 AM
Mister77
Can somebody help..need to compare results as I think the book's wrong!
Hi! Can somebody solve this for me, it's pretty easy, but the result the book gives me seems wrong (or I'm wrong!). I need a second opinion though...here it is:

A man saves 250£ every half-year and invests it at Compound Interest at 4.5 per cent. What will be the amount of his savings in 8 years if the last amount saved bears interest for 6 months?

Thanks for the help everyone!

P.S. The book gives me 4,860£ pounds but as much as I try I get 4,900..
• Feb 26th 2010, 07:41 AM
satx
Write out the formula you used, please...
• Feb 26th 2010, 08:13 AM
Hello Mister77

Welcome to Math Help Forum!
Quote:

Originally Posted by Mister77
Hi! Can somebody solve this for me, it's pretty easy, but the result the book gives me seems wrong (or I'm wrong!). I need a second opinion though...here it is:

A man saves 250£ every half-year and invests it at Compound Interest at 4.5 per cent. What will be the amount of his savings in 8 years if the last amount saved bears interest for 6 months?

Thanks for the help everyone!

P.S. The book gives me 4,860£ pounds but as much as I try I get 4,900..

The vital piece of information that is missing is how often the interest is calculated. If it is every six months (as the question tends to suggest) then the interest payable at the end of every six month period is $2.25\text \%$ of the amount of his savings at the beginning of that period.

At the end of the first six months, he would then have:
£ $250\times(1+ 0.0225)=$ £ $255.625$
before he makes his second investment of £ $250$.

At the end of the next six months he has:
£ $505.625\times(1+ 0.0225)=$ £ $517.0016$
before his next investment; and so on.

Continuing in the same way, at the end of $8$ years, he has £ $4858.26\approx$ £ $4860$.

• Feb 26th 2010, 08:13 AM
Wilmer
Problem is not clear.
Anyhow, future value of 16 deposits of 250 @ 2.25% = 4751.35 :
at this point, last deposit has been made, and has earned no interest.
4751.35 * 1.0225 = 4858.25 : close to your book's of 4860.

how much can be withdrawn 6 months after the last deposit?
• Feb 26th 2010, 12:05 PM
Mister77
Thanks guys, it's like you said, the book isn't clear and I made the mistake of calculating 4.5% on a yearly basis when it should've been 2.25 every 6 months; in my original formula:

(1.045x (1.045 to the power 7 - 1))

divide all that by 1.045-1 and multiply by 500

add the result by 250 and multiply by 1.045

add by 250 again = 4889.

But if I do instead (1.0225x (1.0225 to the power 16 -1)

divide by (1.0225-1) and multiply by 250 = 4860!

I used a geometrical sum formula that I'm sure you're familiar with. Thanks again. Sorry for writing the formula in such an awful way, but I haven't been able to find any special characters button in the message window.