1. Interest MATH 102 Contemporary Math S. Rook

2. Overview Section 9.2 in the textbook: – Simple interest – Compound interest

3. Simple Interest

4. Interest: amount paid in return for borrowing somebody else’s money – e.g. Banks pay you to use your money; You pay credit card companies when you make a purchase on a credit card Simple Interest: given a starting principal P, a rate of growth r, an amount of time t in years: I = Prt – Note that interest is paid only on the initial principal

5. Simple Interest (Continued) Future amount: the total amount of money owed to a borrower over a time period of t years: A = P + I where I is the total amount of simple interest – What is the formula for simple interest? – Simplifies to A = P(1 + rt) – There are four variables in the future amount formula: Given any three, we can solve for the fourth using Algebra

6. Simple Interest (Example) Ex 1: Suppose that $12,000 is placed into an account which pays 5% simple interest annually. If the money is left alone in the account for 8 years: a) Calculate the interest earned (round to the next highest cent) b) Find the total amount in the account

7. Simple Interest (Example) Ex 2: Suppose you wished to save up $10,000 in 10 years by placing money into a CD which pays 4.5% simple interest. How much money would you need to invest in the account to meet the goal (round to the next highest cent)?

8. Compound Interest

9. Recall that simple interest only pays interest on the initial principal – In the real world, interest is compounded (computed) on the current total amount (principal along with interest) Interest is compounded n times per year. n is known as the compounding period r ⁄ n interest is added to the current amount each compounding period – Common compounding periods: annually (1), biannually (2), quarterly (4), monthly (12)

10. Compound Interest (Continued) Formula for compound interest: – Note that this formula is slightly different from the one given in the book Book says to let n = # of compounding periods, but it is easier to compute nt Compound interest formula has four variables – Given the value of any three variables, we can solve for the fourth – Will only be asked to solve for A and P for compound interest

11. Compound Interest (Example) Ex 3: Calculate (to the nearest cent) the amount in the account (round to the next highest cent): a) $5000 invested at 5% compounded annually over 5 years. b) $4000 invested at 8% compounded quarterly over 2 years. c) $20,000 invested at 10% compounded monthly over 4 years.

12. Compound Interest (Example) Ex 4: A mother wishes to establish a $30,000 college fund for her child at the end of 15 years. How much should she initially deposit into an account with a 6% interest rate compounded twice a year to achieve this (round to the next highest cent)?

13. Compound Interest (Example) Ex 5: Suppose you take out a loan for 10 years at a rate of 8.5% compounded monthly. If the total amount to be paid back at the end of the 10 years is $25,000: a) How much did you borrow (round to the next highest cent)? b) How much interest do you pay?

14. Summary After studying these slides, you should know how to do the following: – Calculate values using the simple interest formula – Calculate values using the compound interest formula Additional Practice: – See problems in Section 9.2 Next Lesson: – Consumer Loans (Section 9.3)