4 - 19 While Steve Bouchard was a student at the University of Florida, he borrowed $12,000 in
student loans at annual interest rate of 9 percent. If Steve repays $1,500 per year, how long to the
nearest year, will it take him to repay the loan?
Solution
PMT = $1,500
PVA = $12,000
n=?
r = 9%
Formula:
1
𝑃𝑉𝐴 = 𝑃𝑀𝑇
1−(1+𝑟)𝑛
{
𝑟
}
Or
1
1−(1.09)𝑛
$12,000 = $1,500 {
0.09
}
Or
1−(1.09)−𝑛
$12,000 = $1,500 {
}
0.09
Or
(1.09)−𝑛 = 1 −
$12,000×0.09
$1,500
Or
(1.09)−𝑛 = 0.28
Taking In on both sides:
ln (1.09)−𝑛 = ln 0.28
Or
−𝑛 =
ln(0.28)
ln(1.09)
= −14.77
Or
𝑛 = 14.77 ≅ 15 𝑦𝑒𝑎𝑟𝑠 (𝐴𝑛𝑠)