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# 3.6 – Mathematics of Finance - PowerPoint PPT Presentation

3.6 – Mathematics of Finance. 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

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3.6 – Mathematics of Finance

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## 3.6 – Mathematics of Finance

### 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

### Interest Compounded Annually

Find the amount A accumulated after investing a principal P for t years at an interest rate rcompounded annually.

P = \$12,000, r = 7.5%, t = 7

### Interest compounded k times per year

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

### Interest compounded continuously

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

### 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

Which investment is more attractive, one that pays 8.75% compounded quarterly or another that pays 8.7% compounded monthly?

Comparing annual percentage yields (APYs)

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

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?

### Present Value of an Annuity

You Try! Find the present value (PV) of a loan with an annual interest rate of 4.7%, and periodic payments of \$815.37 for a term of 5 years, with payments made and interest charged 12 times per year.

### 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?

### Homework

Pg.342-343

2, 8, 10, 16, 18, 22, 46, 48