Building: Knowledge, Security, Confidence

Interest Calculations Math

& Science High School

Brian McCulloughStrategic Transactions Group

•An amount of money banks

pay you for keeping money

on deposit with them

Interest

Scenario 1: Ray just got a full-time job and wants to start saving money so he can raise a family. His brother Bill's advice to Ray was to open a savings account so it can accumulate interest.

Scenario 2: Beth does not have enough money to pay for college. She will have to take out student loans from the government. As long as she qualifies, there is no limit to how much she can borrow, but she will have to pay back the loans with interest when she graduates.

Both Beth and Ray’s situations deal with interest.Interest formulas can be quite complicated and difficult to understand. Interest plays a major role in our everyday lives. The simple interest formula is a basic formula that we can use to study interest.

Three things are needed to calculate simple interest:

Principle = the amount put into the bank or the amount borrowed from the bank

Rate = the percent (expressed as a decimal)

Time = how many years the money is in the savings account at the bank or how many years it will take you to pay back the loan.

The tricky part about calculating the interest is the time aspect. The time must be in years. If the time is given in months, simply divide your months by 12. This is because there are 12 months in a year.

Ray put $1,000 into a savings account. The interest on the account is 3.5%. He wants to put the money away for 18 months.

How much will Ray have at the end of that time period? I = p x r x tI = $1,000 x 3.5% x 18I = $1,000 x .035 x 18 (change the percent to a decimal)I = $1,000 x .035 x 1.5(divide the number of months by 12)I = $52.50Adding the interest back on to the principle, Ray now has $1,052.50.

Example

Beth owes $38,000 in student loans. The interest rate on her loans is 8.25%. She will be paying these loans off for 20 years. How much will Beth pay altogether?

I = p x r x t

I = $38,000 x 8.25% x 20

I = $38,000 x .0825 x 20 (change the percent to a decimal)

I = $62,700

Adding the interest back on to the principle, Beth has to pay $100,700.

Compound Interest

• Money you earn on the previously earned interest in your account

• Can be compounded daily, monthly, or annually

The Rule of 72

• How long it will take for your savings to double in value

• What interest rate you need to earn to double your money in a set number of years

Lets you know:

Compound Interest (10%)

Starting Value

Interest Earned

Value at Year End (after

compounding)

Year 1 $100 $10 $110

Year 2 $110 $11 $121

Year 3 $121 $12.10 $133.10

Year 4 $133.10 $13.31 $146.41

Year 5 $146.41 $14.64 $161.05

Year 6 $161.05 $16.11 $177.16

Year 7 $177.16 $17.71 $194.87

Year 8 $194.87 $19.49 $214.36

Total = Principal x (1+ Rate)years

Saving $1 a Day

No Interest

5% DailyCompoundi

ng

5% AnnualCompoundi

ng

Year 1 $365 $384 $383

Year 5 $1,825 $2,343 $2,329

Year 10 $3,650 $6,018 $5,945

Year 30 $10,950 $49,069 $47,325

http://www.1728.com/compint.htm

QUESTIONS/WORKSHEET

Statistics

• 2001 = 83% of college students had at least one credit card:– Average student had four!

• 71% of young adult card holders do not pay off their balance in full each month

• Graduating College seniors had an average of nearly $4,000 in credit card debt:

– 134% from 10 years ago

Statistics (Continued)

• 18-24 year olds declaring bankruptcy 96% increase in the last decade

•

• In 2002:

Congratulations!