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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

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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


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