When you take out a loan, the lender offers a loan amount at a certain annual interest rate and requires a strict payment schedule. Monthly payments are calculated using the formula shown on the figure shown here; the payments always include both principal and interest components. Loan costs are originated from the interest and can be computed as loan costs = (monthly payment x number of months ) - principal. In the steps below, we will consider an example in which you want to calculate the cost of a $15,000 loan over three years at an annual interest rate (AIR) of 6 percent.

#### Step

Calculate the number of months (N) and monthly interest (I). N = 12 x number of years

I = AIR / (12 x 100%)

In our example, this means: N = 12 x 3 = 36 I = 6% / (12 x 100%) = 0.005

#### Step

Calculate the value (1 + I)**N (see figure) first to simplify computing the loan monthly payment (M). S = (1+I)**N In our example, this would be: S = (1+0.005)**36 = 1.06**36 = 1.1967

#### Step

Calculate the monthly payment (M) using the computed value S (see Step 2). M = Principal x (I x S) / (S -1) In our example, this would be: M = $15,000 x (0.005 x 1.1967) / (1.1967-1) = $15,000 x 0.03042=$456.33.

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Calculate the total amount (T) to amortize the loan. Total Amount = Monthly payment x Number of months In our example, this would be: T = $456.33 x 36 = $16,427.88

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Calculate loan costs (C): Loan costs = Total amount - Principal C = $16,427.88 - $15,000 = $1,427.88