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 r compounded 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
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?
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
1 (1 i)
PV  R
i
n
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