Question

What is the annual interest rate of a loan $30000,15 years to maturity and payments of $275/Month?

Answer 1

Loan amount or present value of payment = 30000

years to maturity =15

number of month (n) =15*12 = 180

payment per month (P) = 275

Present value of payment formula = P*(1-(1/(1+i)^n))/i

30000 = 275*(1-(1/(1+i)^180))/i

i is that monthly rate at which PV is equal to $30000

Asssume i is 0.6%

PV = 275*(1-(1/(1+0.6%)^180))/0.60%

=30218.22815

Assume i is 0.63%

PV = 275*(1-(1/(1+0.63%)^180))/0.63%

=29556.37848

interpolaiton formula = lower rate + ((upper rate - lower rate)/(Upper value - lower value)*(Upper value - actual value))

=0.6% + ((0.63%-0.6%)/(30218.22815-29556.37848)*(30218.22815-30000))

=0.006098917395

annual rate = monthly rate * number of months in year

=0.006098917395*12

=0.07318700874 or 7.32%

So annual rate charged on loan is 7.32%