You deposit $9000 in an account earning 5% interest compounded continuously.

Question

The amount of money in the account after T years is given by A(T)=9000e^0.05T

How much will you have in the account in 14 years? round your answer to 2 decimal places.

I got 18123.77437 for the answer.

How long will it be until you have $12400 in the account? round your answer to 2 decimal places.

_____ years

How long does it take for the money in the account to double? round answer to 2 decimal places.

_____ years

Answer 1

9000e^.05(14) = 9000e^.7 = about 18123.77437

rounded to 2 decimals

= $18,123.78

12400 = 9000e^.05t

ln(124/90) = .05t

t = ln(62/45)/.05

t = about 6.409 years to reach $12,400

doubling time is when

2 = e^.05t

ln2 = .05t

t = ln2/.05 =about 13.86 years to double $9000 to $18000 or to double any amount