General Annuity
1. The problem is to find the future value of a general annuity where payments are made at the end of each period.
2. Suppose you make a payment of $P$ at the end of each period for $n$ periods, and the interest rate per period is $i$.
3. The future value $FV$ of this annuity is given by the formula:
$$FV = P \times \frac{(1+i)^n - 1}{i}$$
4. This formula sums the value of each payment compounded to the end of the $n$th period.
5. To solve a problem, you need to know $P$, $i$, and $n$, then substitute into the formula and calculate $FV$.
6. For example, if $P=100$, $i=0.05$, and $n=10$, then:
$$FV = 100 \times \frac{(1+0.05)^{10} - 1}{0.05} = 100 \times \frac{1.628895 - 1}{0.05} = 100 \times 12.5779 = 1257.79$$
7. So, the future value of the annuity is 1257.79.
This is a general annuity problem where payments are made at the end of each period and interest is compounded each period.