Question

You plan to retire in 35 years, and would like to have 1,000,000$ in investments. How much money would you have to invest today at a 7% annual interest rate compounded daily to reach your goal in 35 years. Assume all years have 365 days round your answer to the nearest cent

Answer 1

Given:

You plan to retire in 35 years and would like to have 1,000,000$ in investments.

So, the time = 35 years

And A = 1,000,000

compounded daily, n = 365

Rate of the interest = r = 7% = 0.07

We will find the initial investment = P

We will use the following formula:

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

Substitute with the values of A, r, n, and t

`\begin{gathered} 1000000=P\cdot(1+(0.07)/(365))^(365\cdot35) \\ \end{gathered}`

Solve the equation to find P

`\begin{gathered} 1000000=P\cdot11.5856 \\ \\ P=(1000000)/(11.5856)=86,313.86 \end{gathered}`

So, the answer will be $86,313.86