Question

Part 1-You just inherited $5000. You can invest the money at a rate of 4% compounded monthly. In 10 years, How much will be in the bank?Part 2-Suppose the account in the question above paid continuously instead of compounded monthly. How much will be in the bank after 2 years?

Answer 1

Part 1:

The principal is given $5000. The rate of interest is 4%. The interest is compounded monthly.

The formula of the amount after t years at a rate of r is given below:

`A=P(1+(r)/(12))^(12t)`

The amount after 10 years on the principal $5000, at a rate of 0.04 is calculated below:

`\begin{gathered} A=5000(1+(0.04)/(12))^(12*10) \\ =5000(1+0.003333)^(120) \\ =5000(1.0033333)^(120) \\ =5000(1.4907732) \\ =7453.866 \end{gathered}`

The amount in the bank after 10 years is $7453.866.

Part 2:

The formula of the amount after t years when the interest is compounding continuously is given below:

`A=Pe^(rt)`

The amount after 2 years in the bank is calculated below:

`\begin{gathered} A=5000e^(0.04*2) \\ =5000e^(0.08) \\ =5000(1.08328) \\ =5416.4 \end{gathered}`

The amount after 2 years in the bank is $5416.4.