Question

Suppose that you desire to get a lump sum payment of $100,000 two years from now. Rounded to full dollars, how many current dollars will you have to invest today at a 10 percent interest to accomplish your goal?

Short answer

An amount of $82,645 needs to be invested today to obtain $100,000 after two years.

$$\begin{gathered} Presentvalue=\frac{A}{{\left(1+i\right)}^n} \\ i=RateofInterest \\ i=\frac{10}{100} \\ i=0.1 \\ n=NumberofYearofInvestment \\ n=2 \\ A=Amountaftertwoyears \\ A=\$100000 \\ PresentValue=\frac{100000}{{\left(1+0.1\right)}^2} \\ =\frac{100000}{{\left(1.1\right)}^2} \\ =\frac{100000}{1.21} \\ =\$82644.6281 \\ =\$82645 \end{gathered}$$

The present value will be $82,645.

Step-by-step solution

Step 1. Explanation

The money is to be invested today to get $100,000 after two years is also called present value.

The present value is calculated in the following manner: