Simple Interest

Explanation

Simple interest is earned on the principal only. The amount of interest earned in the first year equals the amount earned in the following years, as long as the initial principal remains invested.

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Simple interest is not an example of an exponential function. Understanding simple interest, though, will shed light on the understanding of compound interest. Compound interest is an example of an exponential function.

Formula symbols:

T	Final value of investment
P	Initial value of investment
n	Number of interest periods, usually number of years
r	Percentage rate per interest period, if per year, the annual percentage rate or APR

At start

T = P

Final value equals initial value.

After 1 period

T = P + Pr = P(1 + 1r)

Final value equals initial value plus one period's worth of interest. Note '1r' in rightmost expression.

After 2 periods

T = P + Pr + Pr = P + 2Pr = P(1 + 2r)

Final value equals initial value plus two periods' worth of interest. Note '2r' in rightmost expression.

After 3 periods

T = P + Pr + Pr + Pr = P + 3Pr = P(1 + 3r)

Final value equals initial value plus three periods' worth of interest. Note '3r' in rightmost expression.

After n periods

T = P(1 + nr)

Note 'nr' in right expression.

Example calculation

If $200 dollars is invested and earns 8.0% APR with simple interest, what is the final value of the investment after 6 years?

T = P(1 + nr)

T = 200(1 + (6)(0.080))

T = $296

Calculator for simple interest

T = P(1 + nr)

T	Final value of investment
P	Initial value of investment
n	Number of interest periods, usually number of years
r	Percentage rate per interest period, if per year, the annual percentage rate (APR)

Enter values below for the above formula. When this page loads, the calculator is set up for a $100 initial investment earning 5.0% for 1 year.

(Example: For r enter 5.0% as 0.05, etc.)

After entering values into the above input areas, click the following 'Calculate' button to get T, the final value of the investment.

Click the following 'Code' button to see the actual JavaScript code that executes in the above calculator. Use this button to see exactly how the above calculator works.

Here's the code that runs when you click the above 'Calculate' button. It is shown here as an aid for your study and understanding.

You can change the code, if you like, and then click the following 'Reevaluate code' button. The program will then work as per your changes when you click the 'Calculate' button on the above calculator. Of course, your changes, especially random changes, can introduce errors, miscalculations, and browser crashes. If you need to get things back to their original condition, just reload this page using your browser's reload button.

Again, the intention here is to conveniently show you the inner workings of this program so that you understand how the program arrives at the result. Click the 'Code' button again to close this section.

window.calculate = function()
{
	var T = 0.0;
	var P = 0.0;
	var n = 0.0;
	var r = 0.0;

	P = parseFloat(document.inputForm.P.value);
	n = parseFloat(document.inputForm.n.value);
	r = parseFloat(document.inputForm.r.value);

	T = P * (1 + (n * r));

	alert("T, final value of investment = " + T);
};