# How to calculate total interest paid on a loan formula?

## Question:

How to calculate total interest paid on a loan formula?

## Interest

There are different ways on how to calculate the interest from a loan. You need to consider what kind of interest is used in your investment or loan.

The following are the most used types of interest you may encounter:

1) Simple Interest

2) Compound Interest

3) Nominal rate of Interest

## Answer and Explanation:

The amount function for the simple, compound and nominal rate of interest are:

Simple Interest:

$$A(t)=P(1+it)$$

where,

{eq}A(t) {/eq} is the accumulated amount of the investment.

{eq}P {/eq} is the amount of investment.

{eq}i {/eq} is the interest rate.

{eq}t {/eq} is the time period.

Compound Interest

$$A(t)=P(1+i)^{t}$$

where,

{eq}A(t) {/eq} is the accumulated amount of the investment.

{eq}P {/eq} is the amount of investment.

{eq}i {/eq} is the interest rate.

{eq}t {/eq} is the time period.

Nominal Rate of Interest

$$A(t)=P\left (1+\frac{i^{m}}{m} \right )^{m\cdot t}$$

where,

{eq}A(t) {/eq} is the accumulated amount of the investment.

{eq}P {/eq} is the amount of investment.

{eq}\frac{i^{m}}{m} {/eq} is the nominal interest rate.

{eq}t {/eq} is the time period.

{eq}m {/eq} is the number of payments.

Now, How do we calculate for the interest?

Example:

For simple interest, what we need is simple algebra:

$$A(t)=P(1+it)$$

$$\frac{A(t)}{P}=(1+it)$$

$$\frac{A(t)}{P}-1=it$$

$$i=\frac{\left (\frac{A(t)}{P}-1 \right )}{t}$$

#### Learn more about this topic:

How to Calculate Interest Expense: Formula & Example

from Financial Accounting: Help and Review

Chapter 5 / Lesson 18
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