Question

Michael wants to save money for his daughters graduation gift. He deposits $775 at the end of each year in an ordinary annuity that pays 4% interest, compounded annually.

Answer 1

we have that

The formula for the future value of an ordinary annuity is equal to:

$FV=P\lbrack\frac{(1+ \frac{r}{n} )^{nt} -1}{ \frac{r}{n} }\rbrack$

where

FV is the future value

P is the periodic payment

r is the interest rate in decimal form

n is the number of times the interest is compounded per year

t is the number of years

In this problem we have

P=$775

n=1

r=4%=0.04

Part a

t=1 year

substitute

$FV=775\lbrack\frac{(1+\frac{0.04}{1})^{(1\cdot1)}-1}{\frac{0.04}{1}}\rbrack$

simplify

$\begin{gathered} FV=775\lbrack\frac{(1+0.04)^1-1}{0.04}\rbrack \\ FV=\ 775 \end{gathered}$

For the first year is the same amount

Part b

For t=2 years

$FV=775\lbrack\frac{(1+\frac{0.04}{1})^{(1\cdot2)}-1}{\frac{0.04}{1}}\rbrack$$\begin{gathered} FV=775\lbrack\frac{(1+0.04)^{(1\cdot2)}-1}{0.04}\rbrack \\ FV=\ 1,581 \end{gathered}$

Part c

For t=3 years

$FV=775\lbrack\frac{(1+\frac{0.04}{1})^{(1\cdot3)}-1}{\frac{0.04}{1}}\rbrack$$\begin{gathered} FV=775\lbrack\frac{(1+0.04)^{(3)}-1}{0.04}\rbrack \\ FV=\ 2,419.24 \end{gathered}$