1. Week 13 Simple Interest

2. Lesson Objectives After you have completed this lesson, you will be able to: Represent or solve simple interest problems. Solve compound interest problems. Write simple and compound interest equations.

3. Interest Interest is the amount charged or earned for borrowing or investing money. When you borrow money from a bank, the bank charges an interest rate on the amount borrowed. When you invest your money, or put your money into an account, the interest earned is the money you make on your investment.

4. Vocabulary Interest – the amount charged to borrow money or earned when investing money. Principal – the original amount deposited or borrowed. Interest Rate – The percent charged to borrow money or earned when investing money. Simple Interest – is the amount paid only on the principal. Compound Interest – is the amount earned on interest and principal. Balance – the principal plus interest

5. Converting % to Decimal In order to calculate interest, we must be familiar with converting percent’s to decimals. To convert a decimal to a percent, simply move the decimal over two places to the right and add a % sign. To change a percent to a decimal do the opposite. Move the decimal over two places to the left and drop the percent sign.

6. Simple Interest The money you initially deposit is called the principal. This also applies to when you borrow money from the bank; the bank collects interest on the loan. One type of interest is simple interest. Simple interest is money paid only on the principal. You can use the following formula to calculate simple interest. I = P * r * t I is the interest earned, P is the Principal, r is the interest rate per year, and t is the time in years.

7. Finding the Interest Rate Use the simple interest formula to find the interest rate. $500 earns $105 in three years, what is the interest rate?

8. Example-2 $800 earns $160 for five years, what is the interest rate?

9. Finding the Principal If the values for interest, rate, and time are given/known, then we can determine the principal. Example What amount must be invested at 5% for one year to earn $75?

10. Finding principal What amount must be invested at 6% for five years to earn $300?

11. Finding the Time If the values for interest, principal, and rate are given/known, then we can determine the time. Example How long must $150 be invested at 5% to earn $300?

12. Example 2 How long must $600 be invested at 5% to earn $120?

13. Example You have invested $600 at the rate of 5%, what is the simple interest earned in 5 year? What would be your current balance?

14. Example $600 invested at the rate of 5%, what is the simple interest earned in 6 months?

15. Simple Interest, Formula: [Loan X Interest Rate (%)] / 12 months = Interest per month. Problem: If you borrow $60,000 at 8% simple interest for five years and pay only interest for the first year, your first monthly payment would be:

16. Compound Interest WEEK 14

17. Compound Interest: When you earn interest on top of interest this is called compound interest. o Interest is added back into the principal and interest is earned from the interest.

18. Example Suppose you deposit $500 in a bank account that earns 4% interest compounded annually (once per year). What is the balance in your account after 4 years? Complete the table below.

19. Complete the table below

20. Formula for compound interest: B = p (1 + r) n B = Balance p = principal, r = annual rate, n = number of periods.

21. Note The rate should be divided by the number of interest periods. The number of interest periods is calculated based on how many times the interest is compounded yearly. Interest compounded semiannually is interest compounded twice per year, so n = 2, and r = annual interest rate/2

22. Example 1: Find the balance on a deposit of $1,500 that earns 6% interest compounded semiannually for 5 years.

23. Example 2 Find the balance on a deposit of $8900 at 9% compounded semiannually for 5 years.