Simple and Compound Interest Unit 4 - Investing

Determining Simple Interest I = p * r * t Interest = Principle X Rate X Time ( in years)

The three things needed to calculate interest… Principle The amount put into the bank or the amount borrowed from the bank Rate The percent 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.

Example #1 Example: 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. Work the equation in your notes

Determine the simple interest for the loan Interest = p x r x t I = $1,000 x 3.5% x 18 I = $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 = $52.50

Find the maturity of the loan… Maturity Value The full amount of money that must be repaid when the loan The principal plus the interest *Determine the interest first, then determine the maturity value by adding the interest to the principal

How much does Ray have to pay back? Adding the interest back on to the principle, Ray now has $1, P+I=MV 1, = 1,052.50

Example #2 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? Work the equation in your notes

How much will Beth pay back all together? 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 MV = $38,000 + $62,700 Adding the interest back on to the principle, Beth has to pay $100,700

Compound Interest Earning interest on interest Remember… Interest =Principle x Rate x Time in years

Example: 2 year period, $4,000 at 6.5% compounded annually Y1: Use Simple Interest equation Y2: Add interest from year one to principle to find out interest earned for year 2 How much will the account have total in the end? How much interest was earned over the two years?

Example: 2 year period, $4,000 at 6.5% compounded annually Y1: P____ x R ______ x T _____ = ____ (Interest Earned) Y2: P____ x R ______ x T _____ = ____ (Interest Earned) End: _______ Total Interest Earned: ______

Example: 2 year period, $4,000 at 6.5% compounded annually Y1: 4,000 x 6.5% x 1 = 260 (Interest Earned) Y2: 4,260 x 6.5% x 1 = End: 4, Total Interest Earned:

Months: Semiannually means you must convert the annual interest rate by 2 times. EX: Interest rate of 6.5% compounded semiannually means the interest rate will be 3.25% since it will be compounded 2 times Quarterly means you must convert the annual interest rate by 4. EX: Interest rate of 12% compounded quarterly means the interest rate will be 3% since it will be done 4 times. If it is done monthly then you would divide the interest rate by 12!

Compounding Interest: Future Value Earning interest on interest “Making your money work for you” A = P (1+ r/n) n*t If you wanted to find out how much you would have after 5 years A is the amount in the account P is the principal (which is the original amount invested) R= the interest rate is expressed as a decimal T= Time in years N= is the number of times it is compounded per year

The power of Compounding: $ earning interest annually ( 1 time a year) Interest Rate1 Year2 years 6.5% A = P (1+ r/n) n*t A = 4000 (1+.065/1) 1*2