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GrogVix [38]
3 years ago
6

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 $
Mathematics
1 answer:
Dominik [7]3 years ago
4 0

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 $\large \boxed{\mathbf{\$4100.07}}$}

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