Nominal
Interest Rate on Investments  Calculation
This
article works on the calculation
of the nominal interest
rate (NIR) for a known initial
investment
which amounts to a known future value in a specified period of time.
The
nominal
rate is usually subdivided for compounding purposes.
The
NIR is based on the following formula:
where:
i = nominal interest rate
P = initial investment
T = future value
N = number of compounding periods per year
Y = number of years
The
nominal rate is expressed as a yearly rate even though the
interest
rate used when compounding interest is i/N. This rate will be
less than the effective interest rate when the interest is compounded
more
than
once a year. That is because the nominal rate stated doesn’t take into
account
interest compounded on interest earned in earlier periods of each year.
The following presentation shows
the main concepts and examples. After this brief presentation, I show
you the coded details.
This is
our simple Matlab code to calculate the NIR formula above:
function it =
nominal_interest_rate(p, t, n, y)
it =
n*((t/p)^(1/(n*y))1)*100;
We create another script
to test and drive the above mfile:
clc;
clear; format bank
p =
input('Enter
principal: ');
t =
input('Enter
total value: ');
y =
input('Enter
number of years: ');
n =
input('Enter
number of compounding periods per year: ');
int_rate
= nominal_interest_rate(p, t, n, y)
Example
1  Investment:
Jean
invests $945 in a savings bank. Four and a half years later her
investment
amounts to $1309.79. If interest is compounded monthly, what is the
nominal
interest rate offered by the bank?
Enter
principal: 945
Enter
total value: 1309.79
Enter
number of years: 4.5
Enter
number of compounding periods per year: 12
The result is:
int_rate
= 7.28
Example
2  Final Value:
David
invests $3000. Ten years later he has earned $1576 in interest. If
interest is
compounded each month, what is the nominal interest rate on the account?
Enter
principal: 3000
Enter
total value: 4576
Enter
number of years: 10
Enter
number of compounding periods per year: 12
The result is:
int_rate
= 4.23
For the effective interest, click
here.
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