Mr. Rosenthal wants to save for a new Kia K5. He expects that it will cost $35 000 four and one-half years from now. How much money will he have to save each year and deposit in a savings account that pays 6⅓% per year, compounded annually, to buy the car in four and one-half years?

Since the interest is compounded only once a year, Mr. Rosenthal will have to accumulate the entire $35 000 during the first four years. Therefore,

Given:

$\mathrm{FV}=\mathrm{35\; 000}$
$i=\mathrm{6⅓\%}$
$t=\mathrm{4½}$ years
$n=4$ deposits

Solution:

$A=\mathrm{\$35,000}(\mathrm{A/F},\mathrm{6⅓}\%,4)=\mathrm{\$35,000}\left[\frac{0.0633}{{(1+0.0633)}^4-1}\right]$

Answer: $A=\mathrm{\$7,650.70}$ per year for four years