Question

You want to buy a car, and a local bank will lend you $10,000. The loan would be fully amortized over 3 years (36 months), and the nominal interest rate would be 15%, with interest paid monthly. What is the monthly loan payment? What is the loan's EFF%?

Answer 1

Loan Amount = 10000

Monthly Interest = 15/12%

Number of Payments = 36

We know that,

Loan Amount = Present Value of all the monthly payments discounted at a monthly rate

10000 = Monthly Payments * ( 1/(1+0.0125)^1 + 1/(1+0.0125)^2 + 1/(1+0.0125)^3 + 1/(1+0.0125)^4 + 1/(1+0.0125)^5 + 1/(1+0.0125)^6 + 1 (1+0.0125)^7 + 1/(1+0.0125)^8 +.................1/(1+0.0125)^36 )

Monthly Payments = $346.65 Answer

Effective Annual Rate = (1+monthly rate)^number of the monthly period in a year - 1

= (1+ 0.0125)^12 -1 = 16.08% Answer

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