Agribusiness Library

LESSON L060021: CALCULATING THE COST OF CREDIT

Objectives1. Define interest, and investigate the factors that determine loan interest rates or the APR.

2. Compare the advantages and disadvantages of fixed and floating loans.

3. Explain how to calculate simple interest.

4. Explain how to calculate compound interest.

Terms•Apr•Compound interest•Fixed loans•Floating loans•Interest•Interest rate•Principal•Rate•Simple interest•Time

Interest is the cost of borrowing money. It is a cost involved when an item is

purchased on credit or with borrowed money, or it can be an income when someone else uses your invested money.

A. Interest rate is the percentage rate that is charged for borrowing money. The annual percentage rate, or APR, is the percentage of

the borrowed amount that will be charged on the loan per year.

There are several factors that will influence the APR.

1. Lending institutions charge interest rates based on the amount of the loan and the length of repayment. Loans that will be repaid in a shorter

amount of time are a better risk for the lender, so these loans may have a lower interest rate.

Large loans that are repaid over many years have a greater chance of not being paid and, therefore, generally have higher interest rates.

2. The federal government adjusts interest rates, and this can affect the typical borrower. As economic conditions worsen,

unemployment tends to rise, which leads to less overall spending.

In these cases, the government can lower interest rates, allowing banks to also lower their interest rates.

The hope is that the decreased interest rates will allow people and businesses to borrow more money to help the economy grow.

Two forms of interest rates on loans are fixed and floating.

A. Fixed loans, or interest rates, are rates that are negotiated at the start of the loan and do not change over the loan’s lifetime. 1. Fixed rates are beneficial for borrowers

who want to lock in a set rate. Therefore, if interest rates begin to rise over time, the fixed rate

loan will not change, which will save the borrower money. 2. On the other hand, if interest rates fall below the fixed

rate, the borrower will not receive the lower rate and will pay more interest than others at that specific time.

B. Floating loans, also known as adjustable rate loans, have an interest rate that can change over the loan’s lifetime. 1. Because this rate can increase as well as decrease and is

fairly unpredictable, it may be an option for borrowers who do not have the credit score to obtain better lending terms.

2. Floating loans can be useful for obtaining loans over a short term, but they must be used wisely with long-term loans. The housing lending crisis of the late 2000s was caused in part

by banks offering adjustable rate loans to borrowers who were unable to repay the loans when interest rates increased.

The two major ways of calculating interest are simple and compound.

A. The simple interest method, also called “add-in interest method,” is calculated by using the original principal for the entire time period (in years) at the determined rate. 1. The formula for calculating simple

interest is simple interest = principal × rate × time. 2. The principal is the total dollar amount borrowed. 3. The rate is the interest rate or percentage charged for

using the principal. 4. Time is the number of years the money is borrowed.

B. Examples of simple interest problems include: 1. Determining the interest amount on $3,000 at 8 percent

interest for one year Step 1: interest = principal × rate × time Step 2: interest = 3,000 × 0.08 × 1

The 8 percent is converted to decimal form (0.08) for the formula.

Step 3: interest = $240 paid for the use of $3,000 for one year

2. Finding the future value of $5,000 invested at 6 percent for three years using simple interest Step 1: interest earned = principal × rate × time Step 2: interest earned = 5,000 × 0.06 × 3 = $900

The 6 percent is converted to decimal form (0.06) for the formula.

Step 3: future value = interest earned + principal FV = $900 + $5,000 FV = $5,900.00

3. Finding the interest on $2,000 borrowed at 9 percent for 73 days Step 1: interest = principal × rate × time Step 2: interest = 2,000 × 0.09 × (73/365)

The 9 percent is converted to decimal form (0.09) for the formula.

The 73 days is converted to years by dividing it by 365 days/year.

Step 3: interest = 2,000 × 0.09 × 0.20 Interest = $36.00

The compound interest method is based on the changing principal balance for the length of time the money is borrowed.

Interest is calculated at specific time intervals during the life of the loan and is added back to the total loan amount.

A. This method results in higher payments. B. This method accrues “interest on interest,” which

results in the principal increasing over the time. Interest is paid more than once during a term.

C. Money can be compounded annually, semiannually, monthly, or daily. Credit cards use compound

interest on balances; this can dramatically increase the total amount owed in a short period of time.

D. The formula for determining future value on compound interest is: future value = present value × (1 + rate) × term.

E. Example of a compound interest problem: 1. An individual invests $1,000 at 8 percent

compounded annually for five years. What is the future value?

Step 1: future value = present value × (1 + rate)n. The reinvested amount is represented as 1 within the

formula; n = number of years.

Step 2: FV = 1,000 (1 + 0.08)5 FV = 1,000 (1.08 × 1.08 × 1.08 × 1.08 × 1.08) FV = 1,000 × 1.46933 FV = $1,469.33

Step 3: The interest earned can be calculated by subtracting the original investment of $1,000 from the future value of $1,469.33. Therefore, the amount of compounded interest earned in

this example is $469.33.

REVIEW•What is interest, and what factors will determine loan interest rates?•What are the advantages and disadvantages of fixed and floating loans?•How is simple interest calculated?•How is compound interest calculated?