Question

Paul Havlik promised his grandson Jamie that he would give him $7,100 7 years from today for graduating from high school. Assume money is worth 8% interest compounded semiannually.
What is the present value of this $7,100? (Use the Table provided.) (Do not round intermediate calculations. Round your answer to the nearest cent.)



Present value $

Answer 1

Answer:

$\large \boxed{\ 4100.07}$

Step-by-step explanation:

The formula for the future value (FV) of an investment earning compound interest is

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

where

PV = the present value (PV) of the money invested

  r = the annual interest rate expressed as a decimal fraction

  t = the time in years

 n = the number of compounding periods per year

Data:

FV = $7100

  r =  8 % = 0.08

  t = 7 yr

 n = 2

Calculation:

$\begin{array}{rcl}\\7100& =& PV \left (1 + \dfrac{0.08}{2} \right )^{2 \times 7}\\\\& =& PV (1 + 0.04)^{14}\\\\& =&PV (1.04)^{14}\\& =& PV(1.731676)\\PV& =& \dfrac{7100}{1.731676}\\\\& =& \mathbf{4100.07}\\\end{array}\\\text{The present value of the money is \large \boxed{\mathbf{\ 4100.07}} }$