 Personal Finance

# Interest Rates and the Time Value of Money

Interest is the price of using money over time, hence it is a direct measure for the time value of money. It is considered an expense to the borrower and income for the lender. Interest is stated as a percentage for a time period (such as 1.5% per month on a credit card or 6% per year on a home mortgage).

• Simple interest is calculated on the original amount borrowed (called the principal). Simple interest is better suited for short-term borrowing and single payment loans than for long-term installment loans.Simple Interest = Principal x Rate x Time
• Compound interest is similar to simple interest, except that interest is earned both on the fixed principal amount and the interest as it accumulates. Saving accounts and mortgages use compound interest, for example. Compound Interest = (Principal x (1 + Rate)Periods) – Principal An alternate way to calculate compound interest is to use the simple interest formula for each period, adding the interest from the previous period to the principal amount for the next period.
• Rule of 78 is a method of computing interest that was popular in pre-computer days. It has since been outlawed in the United States for loans exceeding five years.
• Exact interest treats a year as 365 days.
• Ordinary interest treats a year as 360 days

## Interest Rates

• Periodic Interest Rate is a fractional amount of an annual interest rate. It is the annual rate divided by the number of periods in the year, such as 12 for a monthly rate and 365 for a daily rate. It is multiplied by the average daily balance to calculate periodic interest charges.
• Annual Percentage Rate (APR) is an attempt to standardize the calculation of the cost of borrowing to make comparisons meaningful. APR is an annualized rate that can also include other costs of borrowing in addition to the interest charges. APR does NOT reflect compounding of interest within each year.
• Annual Percentage Yield (APY) is used for comparing investment yields. While APY is similar to APR in that it includes costs of investing, it differs from APR by including the effect of compounding within a year.
• Nominal Interest Rate is the stated interest rate and does not necessarily reflect all the costs of borrowing such as fees, mortgage points, etc.
• Yield curve graphs interest rates on Y axis with term of borrowing (short term vs. long-term) on the X axis:
• upward sloping yield curve – considered normal; has lower interest rates for shorter-term borrowing and higher rates (gradually flattening) for longer terms.
• inverted yield curve – indicates “tight” credit market; has higher interest rates for short-term borrowing and lower rates for longer terms.

## Time Value of Money and other Influences on Interest Rates

Why are some rates higher than others? Why do rates change over time? Interest rates are influenced by:

• Time value of money – This is the ability to get a return on investment, which is in turn influenced by both supply and demand of/for funds and investments, often shown as a rate of return or interest rate.
• Credit risk of the borrower – Some borrowers will default on payments; those with a perceived higher risk are charged a higher rate.
• Inflation risk to the lender – any return to the investor is affected by inflation during the time the funds are loaned; the lender will want to charge a rate that will return the desired rate after inflation, so interest rates should be higher when inflation is expected to be higher or for longer loans that have more risk of inflation than for shorter loans when inflation may be more predictable.