GCR - The Cost of Credit

The Cost of Credit

The cost of credit is the interest paid by the borrower to the lender over the life of the loan. Interest can be calculated as simple interest or compound interest. Each calculation has its own formula as we will see below.

Simple Interest

Where:

I = Interest

P = Principal

R = Rate of Interest

T = Time

For instance, a $500 note at 5% for 2 years would yield

I = $500 x .05 x 2

I = $50

In this case, the borrower would pay back $550 (the $500 borrowed plus $50 interest.)

Compound Interest

A = P(1+R/N)^NT

Where:

A = Total principal and interest

P = Principal

R = Rate of Interest

N= Number of Times Compounded a Year

T = Number of Years

Using our previous example of a $500 note at 5% for 2 years would yield

A = $500(1=.05/1)^1.2

A = $500(1.05)²

A= $500(1.1025)

A= $551.25

In this case, the borrower would pay back $551.25 (the $500 borrowed plus $51.25 interest)

With compound interest, the frequency of compounding can significantly change the amount of interest charged. Using the example above, let's see what would happen if the interest was compounded quarterly or 4 times a year.

A= $500(1 + .05/4)^4.2

A= $500(1 + .0125)⁸

A=$500(1.0125)⁸

A=$500(1.1045)

A=$ 552.25

In this case, the borrower would pay back $552.25 (the $500 borrowed plus $52,25 interest.)

Let's do one more and see if we can spot a trend. Let's assume this time that the compounding is monthly.

A=$500(1 + .05/12)^12.2

A=$500(1+.0042)²⁴

A=$500(1.0042)²⁴

A=$500(1.1058)

A=$552.90

In this case, the borrower would pay back $552.90 (the $500 borrowed plus $52.90 interest).

From these examples, we can come to some conclusions. Three things affect the amount of interest we will repay: Whether simple or compound interest is used, the length of time we take to repay, and the frequency of compounding. The longer the term of the loan and the more frequent the compounding, the more interest you will pay. All other things being equal, you would pay the least amount of interest with the simple interest formula.

For each situation below calculate the total payback (principal +interest) on the loan. 

	Simple Interest	Compound Interest Compounding semi-annually	Compound Interest Compounding weekly
Loan 1 Principal - $5,000 Interest rate - 6% Time - 2 years	$5600	$5627.54	$5637.09
Loan 2 Principal - $10,000 Interest rate - 4% Time - 10 years	$14000	$14859.47	$14915.95

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