# Compound interest & exponential growth/decay. Compound Interest A=P(1 + r ) nt n P - Initial principal r – annual rate expressed as a decimal n – compounded.

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Compound interest & exponential growth/decay

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

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

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

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

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

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?

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?

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