Compound Interest: Formula:
A - represents the amount of money after a certain amount of time
P - represents the Principle - or the money that you start with
r - reprents the interest rate - and is ALWAYS represented as a decimal
t - represents the amount of time in YEARS
n - is the number of times interest is compounded
if interest is compounded annually then n = 1
if interest is compounded quarterly then n = 4
if interest is compounded bi-monthly then n = 6
if interest is compounded monthly then n = 12
Ex 1: Karen has $1,000 that she invests at 3.5% interest compound quarterly. How
much money will Karen have after 5 years?
Look at the formula and see how many values we are given for the variables.
A = unknown
P = $1,000
r = 3.5% = .035
n = 4
t = 5
Then plug these values into the formula and solve for the missing variable (in this case A)
Be careful - Exponents before Mulitplication
After 5 years Karen will have $1,190.34
Ex2: William wants to have a total of $4,000 in two years so that he can put a hot tub on his deck. He
finds an account that pays 5% interest compounded monthly. How much money should William
put into the account so that he has $4,000 at the end of 2 years?
A = $4,000
P = unknown
r = 5% = .05
n = 12
t = 2
William would need to deposit $3,620.10.
Name ______Date ______
Algebra II – Pd ___Applications of Exponential Growth and Decay
1) Karen has $1,000 that she invests at 3.5% interest compound quarterly. How much money will Karen have after 5 years?
2) William wants to have a total of $4,000 in two years so that he can put a hot tub on his deck. He finds an account that pays 5% interest compounded monthly. How much money should William put into the account so that he has $4,000 at the end of 2 years?
3) Kelly plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts it into an account that earns 4.25% interest compounded semi-annually. How much will be in Kelly’s account at the end of four years?
4) You invest $1500 in a savings account earning 6.5% interest compounded annually. How much will be in the account after 7 years, to the nearest cent?
5) You invest $100 in a savings account earning 8% interest compounded quarterly. How much will be in the account after 5 years, to the nearest cent?
6) In 1950 the Population of Fresh Meadows was 23,000. If the growth rate is 1.7%, what was the population in 1975? (Use the formula A = P(1 + r)t since it is not compounded n=1)
7) In 1965, the population of Flushing was 15,000 and in 1980 was 32,000. Find the rate of growth. Use that to predict the population in 2015. (Use the formula A = P(1 + r)t )
8) Radium-226, a common isotope of radium, has a half-life of 1620 years. Professor Korbel has a 120 gram sample of radium-226 in his laboratory. Using the formula A= Pe-0.0004278686t estimate how many grams of the 120 gram sample will remain after 100 years. (to type e into the calculator hit 2nd LN )
9) A company's annual profit of $5,000,000 decreases 2.5% each year for 5 years. What is the approximate annual profit after 5 years? (Use the formula A = P(1- r)t when it is a decrease you change the addition to subtraction)
10) You buy a new car for $25,000. Its value decreases 20% annually. What is its value after 6 years when you want to trade it in? (Again use A = P(1 – r)t )