T 10000 INVESTION 8 INTEREST 3 YRS FIND THE AMOUNT COMPOUNDE

T 10,000 INVESTION, 8% INTEREST, 3 YRS. FIND THE AMOUNT, COMPOUNDED MONTHLY. FIND THE AMOUNT, COMPOUNDED CONTINUOUSLY. HOW LONG WOULD IT TAKE TO DOUBLE, COMPOUNDED CONTINUOUSLY? Radioactive Decay Strontium 90 is a radioactive material that decays according to the function A(t) = A_0 e^-0.02 omega t where A_0 is the initial amount present and A is the amount present at time t (in years). What is the half-life of strontium 90? (ASSUME A_0 = 500 g) Determine how long it takes for 100 grams of strontium 90 to decay to 10 grams. EXTRA CREDIT #1 HOW MUCH MONEY SHOULD BE INVESTED AT 8 1/2% TO HAVE A FINAL AMOUNT OF 20,000, COMPOUNDED MONTHLY. EXTRA CREDIT #2 SOLVE FOR X (3 DECIMALS) 10(8)^X = 8800

Solution

43) A = P (1 + r/n) ^(nt)

Where:

A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

a) A = 10000*(1 + 0.08/12)^(12*3) = $12702.37

b) A = P*e^rt = 10000*e^(0.08*3) = $ 12712.5

c) 20000 = 10000*e^(0.08*t) =========> t = 8.66 years