Download presentation

Presentation is loading. Please wait.

Published byKate Templer Modified over 3 years ago

1
Compound interest & exponential growth/decay

2
Compound Interest A=P(1 + r ) nt n P - Initial principal r – annual rate expressed as a decimal n – compounded n times a year t – number of years A – amount in account after t years

3
Compound interest example You deposit $1000 in an account that pays 8% annual interest. Find the balance after 1 year if the interest is compounded with the given frequency. a) annually b) quarterlyc) daily A=1000(1+.08/1) 1x1 = 1000(1.08) 1 ≈ $1080 A=1000(1+.08/4) 4x1 =1000(1.02) 4 ≈ $1082.43 A=1000(1+.08/365) 365x1 ≈1000(1.000219) 365 ≈ $1083.28

4
Using e in real life. We learned the formula for compounding interest n times a year. In that equation, as n approaches infinity, the compound interest formula approaches the formula for continuously compounded interest: A = Pe rt

5
Example of continuously compounded interest You deposit $1000.00 into an account that pays 8% annual interest compounded continuously. What is the balance after 1 year? P = 1000, r =.08, and t = 1 A=Pe rt = 1000e.08*1 ≈$1083.29

6
Exponential Growth & Decay C = initial population r = rate increase/decrease t = time

7
In1990, the tuition at a private college was $15,000. During the next 9 years, tuition increased by about 7.2% each year. a. Write a model giving the cost C of tuition at the college t years after 1990. b. What is the tuition in 2010? c. What year was the tuition about $20,000?

8
Ex. You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay model for the value of the stereo system in terms of the number of years since the purchase. b.What is the value of the system after 2 years? c.When will the value be less than half?

Similar presentations

OK

If a quantity increases by the same proportion r in each unit of time, then the quantity displays exponential growth and can be modeled by the equation.

If a quantity increases by the same proportion r in each unit of time, then the quantity displays exponential growth and can be modeled by the equation.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on microcontroller based home security system Ppt on observation method of data collection Ppt on network load balancing Ppt on building management system Ppt on types of motion for class 6 Ppt on e marketing Ppt on asp dot net project Ppt on 2d and 3d figures Ppt on active and passive voice 360 degree customer view ppt online