Calculate Annuity - or Future Value of Regular Deposits

where:
T = total value after Y years (future value)
R = amount of regular deposits
N = number of deposits per year
Y = number of years
i = nominal interest rate
 

This is our Matlab function or script to calculate the above formula: 

function t = annuity(r, it, n, y)
it = it/(n*100);
t = r * ((1 + it)^(n * y) - 1)/it;
 

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

clc; clear; format bank

r = input('Enter amount of regular deposits: ');
it = input('Enter nominal interest rate: ');
n = input('Enter number of deposits per year: ');
y = input('Enter number of years: '); 

future_value = annuity(r, it, n, y)

Example 1: 

$50 is transferred each month from Monique’s checking account to a Math Learning Club savings account with 5% interest. How much will Monique receive at the end of the year?
 

We run our test code and get: 

Enter amount of regular deposits: 50
Enter nominal interest rate: 5
Enter number of deposits per year: 12
Enter number of years: 1 

Our result is: 

future_value = 613.94
 

Example 2:

Little George makes annuity payments of $175. The interest is 5.5%. What amount will George have accumulated in 15 years?
 

Again, we run our ‘Calculate Annuity’ code, and get: 

Enter amount of regular deposits: 175
Enter nominal interest rate: 5.5
Enter number of deposits per year: 1
Enter number of years: 15 

The result is: 

future_value = 3921.5

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