Question

Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have $1,000,000 after 40 years with an APR of 5% compounded quarterly. Round your answer to the nearest cent, if necessary.

Answer 1

Given:

There are given that the initial amount, time period, and rate are:

`\begin{gathered} future\text{ value:1000000} \\ time\text{ period:40 year} \\ rate:\text{ 5\%} \end{gathered}`

Step-by-step explanation:

To find the present value, we need to use the present value formula:

So,

From the formula of present value:

`PV=FV(1)/((1+(r)/(n))^(nt))`

Then,

Put all the given values into the above formula:

So,

`\begin{gathered} PV=FV(1)/((1+(r)/(n))^(nt)) \\ PV=1000000(1)/((1+(0.05)/(4))^(4*40)) \end{gathered}`

Then,

`\begin{gathered} PV=1,000,000*(1)/((1+(0.05)/(4))^(4*40)) \\ PV=1,000,000*(1)/((1.0125)^(160)) \\ PV=1,000,000*(1)/(7.298) \\ PV=137023.84 \end{gathered}`

Final answer:

Hence, the amount is $137023.84