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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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By the end of today you will be able to
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



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
Interest compounded for t years at an interest rate k times per year


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


Interest compounded continuously
Interest compounded continuously for t years at an interest rate


You Try! for t years at an interest rate 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
Annual Percentage Yield (APY) for t years at an interest rate

  • 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 for t years at an interest rate 8.75% compounded quarterly or another that pays 8.7% compounded monthly?

Comparing annual percentage yields (APYs)


Ordinary Annuities for t years at an interest rate : 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 for t years at an interest rate : 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
Present Value of an Annuity for t years at an interest rate


You Try! for t years at an interest rate 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
Annual Percentage Rate (APR) for t years at an interest rate

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
Homework for t years at an interest rate

Pg.342-343

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


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