Question

Question: Mrs. Crawford will receive $7,600 a year for the next 19 years from her trust. If a 14 percent interest rate is applied, what is the current value of the future payments?

Short answer

The current value is $49,782.80.

Step-by-step solution

Identification of the required information

Payment (PMT) = $7,600

Period (n) = 19 year

Interest Rate (i) = 14%

Current value (PV)

$$\begin{gathered} \text{PV}\mathbf{=}\text{PMT}\times \left[\frac{1-{\left(1+i\right)}^{-n}}{i}\right] \\ \mathbf{=}\$7,600\times \left[\frac{1-{\left(1+14\%\right)}^{-19}}{14\%}\right] \\ \mathbf{=}\$49,782.80 \end{gathered}$$