Working with interest

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Working with interest

Working with interest

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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 verses loans

A note is usually a short term arrangement whereas a loan is usually a longer term pay back. 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 are 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 (banks, 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 at least two of the three important variables, Time (T), the Interest Rate (R) and the Principal (P).

To compute simple interest the formula is: P X R X 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) X R (.1) X T (60 / 360)* = I 365 day year: P (1000) X R (.1) X 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, which is 60 / 360 using the 360 day year for accounting purposes.

1000 X .1 X .167 = $16.70

It will cost you $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 here and there. 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 to you:

P = I / (R X 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 X (90/360)) = 8000

Finding the Rate

To solve for a missing rate, when the other variables are given to you:

R = I / (P X T)

For example:

You pay $200 in interest to borrow $2000 for one year. What is the interest rate? 200 / 2000 X 1 = 10%

Finding the Time

If you know the interest amount, how much was borrowed and the interest rate, you can then use the following formula to find out how long the money was borrowed:

T = I / (P X R)

For example:

You pay $200 in interest to borrow $2000 with an interest rate of 12%. How long did you borrow the money? 200 / (2000 X .12) = .833333 .8333 X 360 = 300 days