3.6 Math Finance.notebook
October 26, 2015
3.6 Mathematics of Finance
Name: _______________
Objective: Students will be able to use exponential functions and
equations to solve business and finance applications related to
compound interest and annuities.
Interest Compounded Annually
If a principal P is invested at a fixed annual interest rate r,
calculated at the end of each year, then the value of the
investment after n years is: A = P(1 + r)n, where r is a decimal.
Example Suppose Wen Liu invests $500 at 7% interest
compounded annually. Find the value of her investment after 10
years.
Oct 13­3:52 PM
Interest Compounded k times per year
Suppose a principal P is invested at an annual interest rate r
compounded k times a year for t years. Then r/k is the interest
rate per compounding period, and kt is the number of
compounding periods. The amount A in the account after t years
is: A = P(1 + r/k)kt
k
k
k
k
k
=
=
=
=
=
1: ______________
2: ______________
4: ______________
12: _____________
365: _____________
Example Suppose Ginger invests $600 at 9% annual interest
compounded monthly. Find the value of her investment 5 years
later.
Oct 13­4:07 PM
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3.6 Math Finance.notebook
October 26, 2015
Example Shaggy has $500 to invest. What interest rate
compounded quarterly is required to double her money in 10 years?
Interest Compounded Continuously
Suppose a principal P is invested at a fixed annual interest rate r
and is compounded continuously. The value of the investment after t
years is A = Pert.
Example Suppose Anna invests $100 at 8% annual interest
compounded continuously. Find the value of her investment after 7
years.
Oct 13­8:25 PM
Oct 26­7:36 AM
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3.6 Math Finance.notebook
October 26, 2015
In the previous examples, we've made a lump sum deposit. Next,
we'll consider a situation in which regular deposits are made.
An ________ is a sequence of equal periodic payments. We'll only
consider annuities in which the same amount is deposited each
time, which are called ordinary annuities.
Future Value of an Annuity
The future value FV of an annuity consisting of n equal payments of
R dollars at an interest rate i per compounding period is:
FV = R (1 +i)n - 1
i
Example Corey makes a $500 payment into a mutual fund. If his investment
earns 7.88% annual interest compounded quarterly, what will be the value of his
annuity in 20 years?
Oct 13­8:35 PM
The net amount put into an annuity is its present value. The net
amount returned from the annuity is its future value.
How does the bank determine what periodic payments should be?
Present Value of an Annuity
The present value PV of an annuity consisting of n equal payments
of R dollars earning an interest rate i per period is:
PV = R 1 - (1 + i)-n
i
Example Nick purchases a new pickup truck for $18,500. What
are the monthly payments for a 4-year loan with a $2000 down
payment if the annual interest rate is 2.9%?
Oct 13­8:45 PM
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3.6 Math Finance.notebook
October 26, 2015
Assignment: Page 341: 1, 5, 9, 13, 15, 17, 19,
21, 25, 29, 45, 49, 51
Oct 13­10:10 PM
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