# Effective Interest Rate on Investments - Calculation

2.- Examples

4.- Online Calculator (another page within this site)

### 1.- Explanation of concepts and code in Matlab

 This code calculates the effective interest rate for a known initial investment which amounts to a known future value in a specified period of time. This rate expresses the actual rate of interest earned annually on the investment. The effective interest rate is calculated by the following formula:

where:
T = future value
P = initial investment
Y = years

You may calculate the effective interest rate on amounts you have already invested and accrued interest. Or you may calculate the effective interest rate necessary to enable a principal to reach a hypotetical value in a specified amount of time. For example, if you invest \$5000 in a bank and wish \$6800 after six years, you will predict the effective interest rate the bank must pay in order to achieve this.

The effective rate may also be used to calculate the effective percent of depreciation of an investment. A negative rate shows actual depreciation.

This is our simple Matlab code to calculate the formula above:

function eir = effective_interest_rate(p, t, y)
eir = ((t/p)^(1/y)-1)*100;

We create another script to test and drive the above m-file:

clc; clear; format bank

p = input('Enter initial investment: ');
t = input(
'Enter total value after y years: ');
y = input(
'Enter number of years: ');

eir = effective_interest_rate(p, t, y)

### Example 1:

Jane deposits \$945 in a bank. Four and a half years later her account has \$1309.79. What actual percent of her initial investment did the bank pay annually?

Enter initial investment: 945
Enter total value after y years: 1309.79
Enter number of years: 4.5

The result is:

eir = 7.52

### Example 2:

Richie bought a car in 1990 for \$7534.84 and sold it in 1993 for \$3555.00. What was its effective rate of depreciation?

Enter initial investment: 7534.84
Enter total value after y years: 3555
Enter number of years: 3

The result is:

eir = -22.15

### 3.- Video on Interest Rates

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