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:

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

Explanation:

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

So,

From the formula of present value:

$PV=FV\frac{1}{(1+\frac{r}{n})^{nt}}$

Then,

Put all the given values into the above formula:

So,

$\begin{gathered} PV=FV\frac{1}{(1+\frac{r}{n})^{nt}} \\ PV=1000000\frac{1}{(1+\frac{0.05}{4})^{4\times40}} \end{gathered}$

Then,

$\begin{gathered} PV=1,000,000\times\frac{1}{(1+\frac{0.05}{4})^{4\times40}} \\ PV=1,000,000\times\frac{1}{(1.0125)^{160}} \\ PV=1,000,000\times\frac{1}{7.298} \\ PV=137023.84 \end{gathered}$

Final answer:

Hence, the amount is $137023.84