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.
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
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
Whew :)
To find the size of the fund at the end of 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount (size of the fund)
P = the principal amount (amount deposited each time)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Given:
P = $6750 (deposited at the end of each 6 months, so it's semi-annually)
r = 4% = 0.04 (annual interest rate)
n = 2 (compounded semi-annually)
t = 3 years
Now, let's calculate the final amount using the formula:
A = $6750 * (1 + 0.04/2)^(2 * 3)
A = $6750 * (1 + 0.02)^(6)
A = $6750 * (1.02)^(6)
A = $6750 * 1.125508
A ≈ $7593.41
Therefore, the size of the fund at the end of 3 years, when invested at 4% compounded semi-annually, would be approximately $7,593.41.