SOLUTION: Suppose you deposit $1000 in an account with an annual interest rate of 10% compounded quarterly. Use the formula A=P(1+r/n)^nt and round each answer to 2 decimal places, if necess

Question 1160654: Suppose you deposit $1000 in an account with an annual interest rate of 10% compounded quarterly. Use the formula A=P(1+r/n)^nt and round each answer to 2 decimal places, if necessary.
A. Find an equation that gives the amount of money in the account after
t years.
B. Find the amount of money in the account after 9 year.
C. How many years will it take for the account to contain $2000?
D. If the same account and interest were compounded continuously, how much money would the account contain after 9 years?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
A. A=1000(1+(.1/4))^4t units dollars
B. when t=9 A=1000(1.025)^36=$2432.54
C. when A=2000, then 2=(1+.025)^4t
ln2=4t* ln (1.025)
t=ln2/4 ln(1.025)
t=7.018 years or 7 years
Rule of 70 says doubling time in years=70/rate in percent, so 7 years would be expected.
D. A=1000e^(rt)=1000*e(.10*9)
=$2459.60 This is a little above the quarterly amount, and that is what would be expected.

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