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3.6 – Mathematics of Finance

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3.6 – Mathematics of Finance

- 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

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

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

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

- 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?

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.

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?

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