# Compound Interest, Complex and Simple Interest Calculation

In most cases, when you borrow money the lender charges you some form of interest. There are four different types of interest:

• flat charge
• simple interest
• complex interest
• compound interest

Below we explain the way each of the interests work including compound interest formula, as well as the formulas for calculating other interest types.

## Flat charge

The lender simply charges you a set fee to borrow money. This form of interest is almost never used today although it is not uncommon for financial institutions to charge an administration or set-up fee when you borrow money.

## Simple interest

E.g. Simple interest is calculated by multiplying the amount of your debt by the interest rate. This form of interest is often charged by family or friends and not by financial institutions. It isn’t effected by the repayment period. Its a fairly straight forward calculation.

E.g. If you borrow \$5,000 at 10 % simple interest then you would repay \$5,500 (\$5,000 plus \$500 (10 % of \$5,000).

## Complex interest

Complex interest is calculated by multiplying the amount of debt outstanding by the interest rate. The difference here is that the interest rate is applied to the debt at a specific point in time and the amount you pay will depend on the amount of your original loan that remains outstanding. Commercial lenders (banks, finance companies, credit cards, etc) charge this type of interest.

If you borrow \$5,000 at 10% per annum for 36 months your monthly payment would be \$161.34. At the end of the first month you would owe \$41.67 interest (\$5,000 x 10% /12 months). At the end of the second month your loan balance would be \$4,880.33 (\$5,000 + \$41.67 – \$161.34). Your interest charge for the second month would be \$40.67 (\$4,880.33 x 10% / 12 months). By the end of the loan the total interest you would pay is equal to \$808.09.

## Compound interest

Compound interest is the interest charged on any unpaid interest. This is the most expensive type of interest of all. Commercial lenders (banks, finance companies, credit cards, etc) charge this type of interest. The following example explains how to use compound interest formula to calculate the total cost of borrowing if interest is calculated as compound interest.

E.g. Use the same example as above, except you don’t make any payments for 6 months. At the end of the first month you would owe \$5,041.67 (\$5,000 plus unpaid interest of \$41.67). At the end of the second month you would owe \$5,083.68 (\$5,000 plus \$41.67 plus \$42.01 interest). In the second month you paid \$0.34 interest on the unpaid interest from the first month. At the end of 6 months you will owe \$5,255.26 (\$5,000 you borrowed plus unpaid interest of \$255.26). The total cost of borrowing with compound interest, if you then made payments for 36 months, would be \$849.35.

There could be a significant difference in your total cost of borrowing depending on whether compound interest formula or some other type of interest calculation is used. Make certain that you know what rate and what type of interest you are being charged on your debts – take interest in the interest you pay!

## Join the Conversation

1. Mike

What type of interest is a car lease

2. Moneyproblems Answers Post author

Hi Mike. Car leases are a different type of financing altogether. You do pay a form of interest but the calculation is quite different.

Lease payments are based on:
1) paying the difference between the sale price of the lease and the end residual value, over the term of the lease plus
2) paying a monthly financing cost. This financing cost is based on a ‘money factor’ that is actually applied to the full value of the car. It’s a complicated formula. If for example your lease rate is 5%, the money factor would be calculated as 5/2400 or .00208. The monthly lease financing cost would then be calculated as (car price + residual value) * money factor.

In other words, in a lease you are paying:
1) the amount the car is expected to depreciate while you have it
2) a financing fee that is based more on providing a return on the investment the leasing company made in purchasing the vehicle to give to you during the lease.