Question

You have an investment account that has a balance of $50,000. If the account iscompounded daily and has an interest rate of 4%, how much did you originally depositinto the account 10 years ago?

Answer 1

Since we know the future alue of the account, using the formula for the compounded interest with n = 365 (since the account is compounded daily), t=10, r = 4% and A=50000 in the following equation:

`A=P(1+(r)/(n))^(n\cdot t)`

using these values and solving for P, we get:

`\begin{gathered} 50000=P(1+(0.04)/(365))^(365\cdot10) \\ \Rightarrow P=(50000)/((1+(0.04)/(365))^(3650))=33516.74 \\ P=33,516.74 \end{gathered}`

therefore, the original amount deposited 10 years ago is $33,516.74