Question

An initial amount of money is placed in an account at an interest rate of 1% per year, compounded continuously. After six years, there is $1083.07 in the account. Find the initial amount placed in the account. Round your answer to the nearest cent.

Answer 1

We have to find the initial value in the account.

The interest rate is r = 1% = 0.01.

The time period is t = 6.

The final value after 6 years is FV = 1083.07.

The interest is compounded continously.

We can relate the present value PV with the other variables as:

`\begin{gathered} FV=PVe^(rt) \\ PV=FVe^(-rt) \\ PV=1083.07\cdot e^(-0.01\cdot6) \\ PV=1083.07\cdot e^(-0.06) \\ PV\approx1083.07\cdot0.94176 \\ PV\approx1020.00 \end{gathered}`

Answer: the initial amount was $1020.00