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

`\large \boxed{\$4100.07}`

Explanation:

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

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