Initial Investments Formula

The formula used to calculate initial investments is as follows:

 

where:
P = initial investment
T = future value
N =number of compounding periods per year
i = nominal interest rate
 

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

function p = initial_investments(t, n, y, it)
it = it/(n*100);
p = t/(1+it)^(n*y);
 

We create another script to test and run the above m-file. This code starts the previous one: 

clc; clear; format bank 

t = input('Enter total value after Y years: ');
n = input('Enter number of compounding periods per year: ');
y = input('Enter number of years: ');
it = input('Enter nominal interest rate: '); 

init_invest = initial_investments(t, n, y, it)

Example 1:

How much should you invest at 8.5% to produce 10000 at the end of 10 years if interest is compounded quarterly? 

Let’s launch our program here... 

Enter total value after Y years: 10000
Enter number of compounding periods per year: 4
Enter number of years: 10
Enter nominal interest rate: 8.5

The result is: 

init_invest = 4312.38

Example 2:
 

A savings company wishes to sell a bond which will be worth $5000 five years from the purchase date. Interest will be 7.9% compounded daily. How much must the bank charge for the bond?

Enter total value after Y years: 5000
Enter number of compounding periods per year: 365
Enter number of years: 5
Enter nominal interest rate: 7.9
 

The result is:

init_invest = 3368.54