Question

Effective Rate of Interest A mortgage company offers to lend you $85,000; the loan calls for payments of $8,347.06 at the end of each year for 30 years. What interest rate is the mortgage company charging you? Do not round Intermediate calculations. Round your answer to two decimal places

Answer 1

This can be solved using the Present value of annuity formula

Present value of annuity is = P*(1-(1+r)^-n)/r

"P" is Payment at the end of each year = $ 8,347.06/.

Present value of annuity is = $ 85,000

"r" is Effective interest rate = ?

"n" is No of years = 30

85000=8347.06*(1-(1+r)^-30)/r

(1-(1+r)^-30)/r=(85000/8347.06)

(1-(1+r)^-30)/r=10.18322619

(1-(1+r)^-30)=10.18322619*r

Using trial and error, r is = 9.10% Approx.

Answer is 9.10% Approx.