Question

A man will deposit 6750 in a fund at the end of each 6 months for 10 yrs. Find the size of the fund at the end of 3 yrs if it is invested at 4% compounded semi annually.

Answer 1

at the end of
6 mo, the fund has 6750
1 yr, 6750*1.02 + 6750
1.5 yr, 6750*1.02^2 + 6750*1.02 + 6750
At the end of 3 years (6 periods) that will be
6750*(1.02^6-1)/(1.02-1) = 42579.82

Answer 2

I assume you mean 2% every six months or half year
so 3 years is 6 periods at 2%
This is sometimes called amount of an annuity
6750 * [ (1.02)^6 -1 ] /0.02
= 6750 * [ .126/.02]
=6750 * 6.308
=42,579.82

Answer 3

Whew :)