HEVT - Simple Interest Loans Lesson

Simple Interest Loans

Introduction

There are many things in life that are too expensive to buy outright with cash. Want to buy a car someday? Cars can cost upwards of $25,000. This is not typically an amount of money that sits in someone's bank account. How about a house? Depending on where you live, you may not be able to find a house that cost less than $300,000. Secondary education, like a college or vocational school, can cost thousands of dollars as well. So, how do people afford these necessities?

Most people will not have even close to that amount of money available in cash. This is where loans come into play. With a loan, you initially borrow a certain amount of money and are obligated to pay it back at a later time. Usually, this involves a monthly payment AND added fees and interest.

Let’s take a look at some of the concepts that go into these loans so that we are able to make better decisions when deciding to borrow some money.

Single Payment Loans

A loan is money you have borrowed and must repay with interest. One type of loan is a single-payment loan. This type of loan is repaid with a single payment after a specified period of time. An example of a single-payment loan is a promissory note. The maturity value of a loan is the total amount you repay. This includes the amount you have borrowed or the principal and the interest owed.

Maturity Value = Principal + Interest Owed

The term of the loan is the length of time for which the loan is granted. This can be years, months, or days. When a term is a certain number of days, interest can be calculated using the following formula.

Interest Owed = Principal x Rate x Time (# of days ÷ 365 days)

Example 1: Joan was granted a loan for $4,600.00 for 103 days at an interest rate of 14%. What is the interest owed and what is the maturity value?

Interest Owed = Principal x Rate x Time (# of days ÷ 365 days)
Interest Owed = $4,600 x 14% x (103 ÷ 365)
Interest Owed = $4,600 x 0.14 x 0.28219
Interest Owed = $181.73

Maturity Value = Principal + Interest Owed
Maturity Value = $4,600 + 181.73
Maturity Value = $4,781.73

Example 2: Try this one on your own and then check your answer below. You were approved for a loan of $2,500.00 for 167 days at an interest rate of 22%. What is the interest owed and what is the maturity value?

Interest Owed = Principal x Rate x Time (# of days ÷ 365 days)
Interest Owed = $2,500.00 x 22% x (167 ÷ 365)
Interest Owed = $2,500.00 x 0.22 x 0.4575
Interest Owed = $251.63

Maturity Value = Principal + Interest Owed
Maturity Value = $2,500.00 + $251.63
Maturity Value = $2,751.63

Allocation of Monthly Payments

The amount of interest you pay depends on the principal amount owed. The interest is computed every month. Your payment for each month includes an interest payment as well as a payment to your principal balance.

Monthly Payment = Payment to Principal + Interest Payment

Interest = Principal x Periodic Rate

Example 1: Diana decided to buy a new car. Once she made her down payment, she had to finance $20,000. The APR is 8% and her monthly payments will be $488.26. Diana wants to calculate the interest and principal payment for her first payment. What is the interest? What is the payment to the principal? What is the new principal after the payment?

If the APR is 8%, then the monthly periodic rate is 0.08/12 = 0.0067

Interest = Principal x Periodic Rate
Interest = $20,000 x 0.0067
Interest = $134.00

The monthly payment covers the $134.00 interest charge and there is $488.26 - $134.00 = $354.26 left that goes towards the principal. This means that after this payment, the new principal will be $20,000 – $354.26 = $19,645.74.

Example 2: Try this one on your own and then check your answer below. You finance $15,500 for a car. The APR is 7.25% and the monthly payments are $375.25. How much of your first payment goes towards the interest? How much goes towards the principal? What is the new principal after the payment?

If the APR is 7.25%, then the monthly periodic rate is 0.0725/12 = 0.0060

Interest = Principal x Periodic Rate
Interest = $15,500 x 0.0060
Interest = $93.00

The monthly payment covers the $93.00 interest charge and there is $375.25 - $93.00 = $282.25 left that goes towards the principal. This means that after this payment, the new principal will be $15,500 – $282.25 = $15,217.75

Simple Interest Practice

1. John has a single-payment loan for $7,500. The interest rate is 13% for 135 days.

What is the interest owed?
What is the maturity value?

2. Amari financed $1,680.00 with an APR of 20%. Her monthly payments are $85.51.

How much interest will she pay in her first payment?
How much of her first payment will be applied to the principal?
What is the new principal amount after her first payment?

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

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