Question

Suppose you borrow $20,000 and then repay the loan by making 12 monthly payments of $1,492.92 each. What rate will you be quoted on the loan?

Answer #1

We can use the NPV method

So NPV of borrowing = 20000

NPV of each of the payments considering monthly compounding = 1492.92 / (1+r/1200)^1 + 1492.92 / (1+r/1200)^2 + ... + 1492.92 / (1+r/1200)^12

Let 1 / (1+r / 1200) = x

NPV of payments = 1492.92x * (x^12 - 1) / (x-1)

So 1492.92x * (x^12 - 1) / (x-1) = 20000

Solving we get x = -1.30614

or 1/ (1+r/1200) = -1.30614

or 1+r/1200 = -0.76561

or r/1200 = -1.76561

or r = -2118.74

So the rate of interest that would be quoted will be -2118.74%.

Please note that the total payment done would be 1492.92 * 12 = 17915.04 which is less than the amlount borrowed of 20000.

This means the rate of interest must be negative.

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