1. Today in Precalculus Turn in graded worksheet
Notes: Mathematics of Finance (need a calculator)
Interest rates
Annual Percentage Yield
Homework

2. Compound Interest Compound interest: A: final amount P: principal
r: interest rate
k: number of payments per year
t: number of years

3. Example 1
P=$18,000
k = 2
t = 6
r= 0.075
=$27,998.18

4. Example 1b P=$18,000 k = 4 t = ? r= 0.075 A=$27,000
log1.5 = 4tlog
4t=21.827
t = years

5. Example 1c A=$31,500 P=$18,000 k = 12 t = 15 r= ? r = .0374
So an interest rate of 3.74% is required.

6. Continuously Compound Interest
Continuously Compounded interest: A=Pert
A: final amount
P: principal
r: interest rate
t: number of years

7. Example 2
P=20,000
t = 8
r = 0.053
A=20,000e(8•.053)
= $30,561.23

8. Example 2b t = 30.367 years 100,000 = 20,000e.053t 5 = e0.053t
ln5 = 0.053t
A = $100,000
P = $20,000
r = 0.053
t = ?
t = years

9. Example 2c 40,000 = 20,000e10r 2 = e10r ln2=10r r =.0693
t = 10
40,000 = 20,000e10r
2 = e10r
ln2=10r
r =.0693
An interest rate of 6.93% is needed

10. Annual Percentage Yield (APY)
A common basis for comparing investments with different interest rates and methods of compounding.
The percentage rate that, if compounded annually, would yield the same return as the given interest rate with the given compounding.

11. Example 1
Bob invests with the local bank at 2.12% interest compounded monthly. What is the equivalent APY?
So the APY is 2.14%.
This means his investment compounded monthly at 2.12% earns the same interest as if it earned 2.14%, compounded once a year.
=.0214

12. Example 2
Which investment is more attractive, one that pays 8.5% compounded quarterly or another that pays 8.45% compounded monthly?
x=.0877
x=.0879
So the investment with the 8.45% rate compounded monthly is the better investment

13. Example 3
The interest charge by your credit card company is 18.75% APY. What is the monthly interest charge on a balance of $5,000?
r = .1731
$5000x.1731 = $865.43

14. Homework
Pg 341: 3-9 odd, 21-39odd, 41-46all