1. 3.6 – Mathematics of Finance

2. By the end of today, you will be able to:
Find the value of an investment in which interest is compounded annually, a specified amount of times per year, and continuously
Compute and Compare Annual Percentage Yields
Calculate the Present and Future values of an annuity

3. Interest Compounded Annually

4. Find the amount A accumulated after investing a principal P for t years at an interest rate r compounded annually.
P = $12,000, r = 7.5%, t = 7

5. Interest compounded k times per year

6. You Try! Find the amount A accumulated after investing $1500 for 5 years at an interest rate of 7% compounded quarterly.

7. Interest compounded continuously

8. You Try! Find the amount A accumulated after investing a principal amount of $1250 for 6 years at interest rate of 5.4% compounded continuously

9. Annual Percentage Yield (APY)
Used to compare investments
It is the percentage rate that, compounded annually, would yield the same return as the given interest rate with the given compounding period

10. Comparing annual percentage yields (APYs)
Which investment is more attractive, one that pays 8.75% compounded quarterly or another that pays 8.7% compounded monthly?

11. Future Value of an Annuity
Ordinary Annuities: A sequence of periodic payments made at the end of each period at the same time the interest is posted in the account.
Future Value of an Annuity

12. An IRA Account: Amy contributes $50 per month into the Lincoln National Bond fund that earns 7.26% annual interest. What is the value of Amy’s investment after 25 years?

13. Present Value of an Annuity

14. You Try! Find the present value (PV) of a loan with an annual interest rate of 4.7%, and periodic payments of $ for a term of 5 years, with payments made and interest charged 12 times per year.

15. Annual Percentage Rate (APR)
The annual interest rate charged on consumer loans Ex) What is Kim’s monthly payment for a 4-year $9000 car loan with an APR of 7.95% from Century Bank?

16. Homework
Pg , 8, 10, 16, 18, 22, 46, 48