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Interest Rate Calculations Applicable To Loans

Interest rates play a pivotal role in the economy and financial markets. They exert a profound impact on many of the financial decisions we make as consumers (e.g., choosing among various types of checking and savings accounts in order to get the best rate possible, selecting a mortgage or applying for a loan in order to finance the purchase of an automobile). Interest rates are of keen interest to borrowers who, of course, want to know the “true” extent of their financial obligations (i.e., or, exactly how much interest they are being charged). The following interest rate calculations may be of help when analyzing the feasibility of a loan that is consistent with one’s needs, objectives, ability for repayment and time horizon.

I. Simple Interest Calculation

The following example illustrates the calculation of simple interest. Multiply the principal by the interest rate and the time. This formula is useful when the principal plus interest have to be repaid in one lump sum.

Principal x Rate x Time = Interest

P = Principal
R = Rate as presented in decimal form (per year)
T = Time
I = Interest

Example: $200 (Principal) at 0.06% (Rate) per year (Time).

I = P x R x T

I = 200 x 0.06 x 1 = $12

Amount (A) = P + I

A = 200 + 12 = $212 = The lump sum to be repaid (principal + interest).

II. The Annual Percentage Rate (APR)

There are times when the loan is repaid in a given number of installments of a specific dollar amount at a mutually agreed upon interest rate. In such a case, the true annual percentage rate of interest (APR) will always be higher than the pre-determined interest rate.

Example: An individual borrows $2500 at 8% interest and must repay the loan (principal + the interest) in 12 monthly installments of $225.00. What is the true annual rate of interest (APR) that is being charged on the loan?

The formula:

N = the number of scheduled payments per year (twelve if paid on a monthly basis or fifty-two if paid weekly)
P = Principal (amount borrowed)
S = interest rate agreed between the borrower and the lender
D = dollar cost per year given the agreed upon interest and the principal (S x P)
R = APR (the true annual percentage rate of interest)

The formula in this case is:

R = 2 x N x (S x P) ÷ P (N + 1)

N = 12
S = 0.08
P = $2500

R = 2 x 12 x (.08 x 2500) ÷ 2500 (12 + 1)

= 4800 ÷ 2500 x 13

= 4800 ÷ 32500

= 14.77% (rounded)

Very often loans may be repaid in monthly installments of given dollar amounts. As can be ascertained with this example, the APR (i.e., the true annual percentage rate of interest) is always higher than the mutually agreed upon interest rate; 14.77% > 8%).

For informational purposes only.

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