Working with Interest
Working with Interest
When individuals or companies borrow money, they are usually charged interest. Interest is the cost to borrow the money. Interest is computed as a percentage and is usually given in terms of an annual percentage rate (APR).
Interest can also be earned when money is deposited in an interest-bearing account. Both borrowers and lenders are concerned about interest, as you can either earn interest or pay interest.
Notes Versus Loans
A note is usually a short-term arrangement, whereas a loan is usually a longer-term repayment arrangement. Notes are paid back all at once, with interest, when they are due. Loans are amortized with payments being made throughout the loan term until the balance is paid off.
A corporate or municipal bond could be considered a note rather than a loan. A mortgage or car loan would be amortized as a loan.
360-Day Year
Because notes are often terms of days—30, 60, 90, and such—interest for corporate and municipal bonds is computed as if a year has only 360 days. This makes computing interest for a period of less than one year much easier.
365-Day Year
Government bonds and consumer lending agencies such as banks and mortgage companies use the actual 365-day year for computing interest.
Principal
Principal is the amount of money borrowed or lent.
Time
When computing interest, you must know the time for which interest is charged. With a note, the interest is usually charged on the entire principal. With loans, the principal changes each time a payment is made.
Computing Interest
To compute interest (I), you must know the three important variables: Time (T), the Interest Rate (R), and the Principal (P).
To compute simple interest, the formula is:
P × R × T = I
For example, if you borrow $1,000 at 10% for 60 days, how much do you have to pay in interest?
360-day year: P (1000) × R (.1) × T (60 / 360) = I
365-day year: P (1000) × R (.1) × T (60 / 365) = I
Notice that the time is computed in terms of a fraction of a year. The interest rate is for an entire year. You are not borrowing the money for an entire year, just 60 days.
Using a 360-day year:
1000 × .1 × .167 ≈ $16.70
It will cost about $16.70 to borrow the $1,000 for 60 days at 10% interest.
If you use a spreadsheet or calculator and compute to more decimal places, your answer may vary by a few pennies. This is especially true if you use a 365-day year.
Finding the Principal
If you know the interest rate, the amount of interest, and the time, you can find the principal if it is not given:
P = I / (R × T)
For example, if you paid $200 in interest for a 90-day note at a rate of 10%, how much did you borrow?
200 / (.1 × (90/360)) = 8000
Finding the Rate
To solve for a missing rate when the other variables are given:
R = I / (P × T)
For example, you pay $200 in interest to borrow $2,000 for one year. What is the interest rate?
200 / (2000 × 1) = .10 = 10%
Finding the Time
If you know the interest amount, how much was borrowed, and the interest rate, you can use the following formula to find how long the money was borrowed:
T = I / (P × R)
For example, you pay $200 in interest to borrow $2,000 with an interest rate of 12%. How long did you borrow the money?
200 / (2000 × .12) = .833333
.8333 × 360 ≈ 300 days