Question

It is a fact that (1 + 0.12)3 = 1.40. Knowing that to be true, what is the present value of \(140 received in three years if the annual interest rate is 12 percent?

1. \)1.40

2. \(12

3. \)100

4. $112

Short answer

Option (c) $100

Step-by-step solution

Step 1. Meaning and formula for the present value

The present value method says that the current value of the amount received in the future is the ratio of the future amount to the compound interest gained over the years.

$X_0=\frac{X_t}{{\left(1+i\right)}^t}$

X₀ is the present value of the future amount, i is the interest rate, t is the time, and X_t is the amount received after t years.

Step 2. Calculations for the answer

Given that $140 will be received after 3 years along with the compound interest charged by 12% annually, the present value of $140 is:

$$\begin{gathered} X_0=\frac{140}{{\left(1+0.12\right)}^3} \\ =\frac{140}{1.40} \\ =100 \end{gathered}$$

Hence, the answer is $100.