Debt

In my last writing, Post 1 of this series, the detail and math concerning continuously compounded interest was explained.  Please read Post 1, to get the fundamentals of compounding interest before reading this writing on interest on loans. Savers and lenders benefit from continuously compounded interest. This post will focus on the different types of debt and how interest is calculated and charged for each. The interest on loans for commonly sought loans can be broadly categorized into two main types that charge interest differently, these two categories are simple interest and compounded interest loans.

Compounded Interest

The most penal type of compounded interest for borrowers is credit card debt. Think of credit card debt as system designed to take money out of your pocket as fast as possible. This is done by compounding the interest, but also from the terms and conditions that a consumer is subject to when they agree to take a loan from a credit card company. A hypothetical credit card example, called Hypo Card, will be used to describe the cost of taking credit card debt. Hypo Card charges an Annual Percentage Rate (APR) of 20%. This 20% quoted rate is not the compounded rate even though credit card companies compound interest daily. Government regulations require that Hypo Card give consumers a 21-day grace period from the time of the statement until payment is due. They cannot charge interest on purchases during the grace period, but there is a catch!

The business terms of the card dictates that if after the grace period has expired, a balance payable exist, meaning you did not pay the balance in full, Hypo Card can charge interest, compounded daily on the balance amount as well as any new purchases from the day it is charged to the card. Effectively, if you have a balance on your credit card the grace period goes away. You must pay the balance in full for two months consecutively to get the 21-day grace period back! Let’s now talk about that 20% interest rate.

All credit card companies compound interest daily on any balance after the grace period as well as any new purchases made if you have a balance. Using the knowledge learned in Part 1 of this series, the true compounded rate can be calculated. Below is an example for the calculation. Hypo Card has \$1,000 balance with a 20% APR interest rate compounded daily.

\$1,000(1+(.20 APR)/(365 Days) )^(365 Days)=\$1,221.35

(\$221.35 Interest)/(\$1,000 Balance)=22.14% Annual Interest Charged

Clearly the true interest rate is not 20% but 22.14%.  A \$1,000 balance held at 22.14% interest doubles to \$2,000 in 38 months, a bit smidge over 3 years.  If a credit card must be used, pay the balance in full during the 21-day grace period to avoid usurious interest charges.

Simple Interest

Thankfully car and mortgage loans do not charge compounded interest but simple interest. Simple interest is the actual annual rate. The calculation for savings is easy:

Amount=Principal*rate*years

The calculation for a borrower is best explained by an example. Let say you borrow \$20,000 to buy a car and the lender is going to charge you 5% simple interest for three years. You will pay back the loan monthly so the interest will be amortized. The payment calculation is:

Payment=  (Loan Amount x interest rate(1+interest rate)^(Number of payment periods))/((1+interest rate)^(number of payment periods)-1)

Interest Rate 5%/100/12 months= .004167 interest rate per month

Number of payment periods= 12x 3 years= 36 months

Loan amount-\$20,000

\$559.42 monthly payment=(\$20,000*.004167(1+.004167)^36)/((1+.004167)^36-1)

The total amount paid is calculated by multiplying the payment by the number of payment periods. \$559.42 x 36 months= \$20,139.12

The amount of interest is calculated by subtracting the amount borrowed from the total amount paid: \$20,139.12- \$20,000= \$139.12 interest paid.

Since the amount borrowed and subject to interest decreases with each payment made, the interest paid is also decreased over time.

Simple interest is the most transparent and understandable form of interest. Mortgages and car loans are typically based upon simple interest calculations. Always check the terms and conditions of the loan to determine the true cost. Can you pay off the loan early without penalty, what are the late fees, can the loan be assumed, etc.

Avoid credit card interest by paying off your balance before the grace period. If you need to borrow money borrow under a simple interest loan and make sure you get a low rate, pay it off as fast as you can, and check to understand the terms and conditions of the loan.