You have an outstanding student loan with required payments of $500 per month fo

Question

You have an outstanding student loan with required payments of $500 per month for the next four years. The interest rate on the loan is 9% APR (compounded monthly). Now that you realize your best investment is to prepay your student loan, you decide to prepay as much as you can each month. Looking at your budget, you can afford to pay an extra $150 a month in addition to your required monthly payments of $500, or $650 in total each month. How long will it take you to pay off the loan? (Note: Be careful not to round any intermediate steps less than six decimal places.) The number of months to pay off the loan is(Round to two decimal places.)

Explanation / Answer

Firstly we have to calculate the principle loan amount ...... i.e present value of $ 500 per month for 48 months ( 4 years )

n = 48, r = 0.09/12 .......... so PVIFA = [ 1 - (1+r)-n ] / r = [ 1 - (1.0075)-48 ] / 0.0075 =  40.184782

Principle loan amount = 40.184782 * 500 = 20092.39

Now instead of $ 500, we will be paying $ 650. and n = ? ( unknown) but r = 0.09/12 = 0.0075

650 * [ 1 - (1.0075)-n ] / 0.0075 =  20092.39

[ 1 - (1.0075)-n ] = 20092.39 * 0.0075 / 650 = 0.23183528

(1.0075)-n = 1 - 0.23183528 = 0.76816472

- n * Log (1.0075) = Log ( 0.76816472)

- n * 0.00324505 = - 0.11454564

n = 0.11454564 / 0.00324505 = 35.30 months ......... final answer

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.