# 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.)

P: n: r:

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

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