Question

# Allysha just borrowed 39,900 dollars. She plans to repay this loan by making a special payment...

Allysha just borrowed 39,900 dollars. She plans to repay this loan by making a special payment of 5,000 dollars in 5 years and by making regular annual payments of 7,900 dollars per year until the loan is paid off. If the interest rate on the loan is 4.79 percent per year and she makes her first regular annual payment of 7,900 dollars in one year, then how many regular annual payments of 7,900 dollars must Allysha make? Round your answer to 2 decimal places (for example, 2.89, 14.70, or 6.00).

Solution

Loan amount= 39900

Loan amount shoul be equal to Present value of 5000+Present value of annuity of annual payments of 7900

PV of annuity =Annual payment*((1-(1/(1+r)^n))/r)

Where

r= interest rate per period=4.79%

n=number of periods

Annual payment=7900

PV of annuity =7900*((1-(1/(1+.0479)^n))/.0479)

Present value of 5000=5000/(1+r)^n=5000/(1+.0479)^5=3957.043

Loan amount shoul be equal to Present value of 5000+Present value of annuity of annual payments of 7900

39900=3957.043+7900*((1-(1/(1+.0479)^n))/.0479)

Solving we get n=5.2537

Thus the number of payments=5.25