Chapter 8.3, Problem LC

(a)

To determine

To calculate: The amount of first deposit at the time of last deposit when $R$ dollars are deposited at the beginning of each period for $n$ periods.

(b)

To determine

To calculate: A series for the total amount of all $n$ deposits at the time of last deposit if the annuity consists of periodic payments into an account paying compound interest and $R$ dollars is deposited at the beginning of each period for $n$ periods and the compound interest rate is $i$ per period.

(c)

To determine

To prove: The sum of the series for the total amount of all $n$ deposits at the time of last deposit is $\frac{R\left({\left(1+i\right)}^n-1\right)}{i}$.

(d)

To determine

To calculate: The amount at the time of the last deposit for an annuity of $\$2000$ per year for $30$ years at $12\%$ compounded annually.

(e)

To determine

To calculate: The amount $7$ months after the last deposit for an annuity of $\$800$ per month for $13$ years with a rate of $9\%$ compounded annually.