# Small Basic – Compound Interest Example

Let’s Make Money

Let's say you invested \$100 in a project that yields 2% at regular periods of time. The Table shows how your money grows over time.

Table: How your money accumulates

 After You’ll have Also equals 1 period 100 + (0.02 ´ 100) = 102 100 ´ (1+0.02)1 2 periods 102 + (0.02 ´ 102) = 104.04 100 ´ (1+0.02)2 3 periods 104.04 + (0.02 ´ 104.04) = 106.12 100 ´ (1+0.02)3 …

This is the idea of compound interest; you gain interest on the interest! (Surprise your parents by asking them if they’re compounding their interest!) The starting amount (the \$100 in this example) is the principal. How often the interest is compounded is up to the bank! For example, they can do it four times a year (called quarterly compounding), 12 times a year (called monthly compounding), or even 365 times a year (called daily compounding).

In this example, you’ll write a program that calculates the compound interest on a principal (P) at an annual interest rate (R). The interest is compounded quarterly for Y years. The complete program’s in the Listing. Save the program as CompoundInterest.sb.

Listing: Using a For loop to track compound interest

1 ' CompoundInterest.sb

2 ' Computes the compound interest

3

4 P = 4000    'Principal = \$4000

5 Y = 10      '10 years

6 R = 0.04    'Annual Interest rate = 4%

7 R = R/4     'Interest rate per quarter

8

9 For N = 1 To (Y * 4) 'Loops for the number of quarters

10   I = R * P     'Calculates the interest this quarter

11   P = P + I     'Adds the interest to the principal

12 EndFor

13

14 P = Math.Round(P) 'Rounds the answer

15 TextWindow.Write("You'll have \$" + P)

16 TextWindow.WriteLine(" after " + Y + " years.")

The program starts by initializing the values of P, Y, and R (Lines 4-6). The short variable names in this example are okay because they don’t affect the program’s clarity. In Line 7, the program divides the interest rate by 4 to get the interest rate per period (for each quarter). The program then starts a loop than runs for (Y*4) periods, because the interest is compounded quarterly (Line 9). In each iteration, the program calculates the interest and adds it to the principal (Lines 10-11). When the loop ends, the program rounds the answer (Line 14) and displays the result (Lines 15-16):

You'll have \$5955 after 10 years.

TIP: Although we usually set the loop parameters to constants values, the initial and terminal values in a For loop can be any Small Basic expression. Line 9 uses the expression (Y * 4) as the For loop’s terminal value.

TRY IT OUT!

Update the Listing to read the interest rate from your user. Run the program for these interest rates: 3%, 3.5%, 4.5%, 5%, and 6%. If you were able to invest your \$4000 at 6% interest rate, can you find out how many years it would take you to become a millionaire? Hint: try different iteration counts in the For loop until your money exceeds \$1,000,000.

Small and Basically yours,

- Ninja Ed & Majed Marji

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