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Paul Palumbo assumes that he will need to have a new
roof put on his house in four years. He estimates that
the roof will cost him $18,000 at that time. What
amount of money should Paul invest today at 8%,
compounded semiannually, to be able to pay for the
roof?
O $13,152.60
$24,634.80
$15,431.40
O $ 9,725.40
O none of the above​

Respuesta :

lucic

Answer:

$13,52.60

Step-by-step explanation:

The formula to apply is

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

where

A= amount of money at the end

P=the amount of money to invest, principal

r=rate of interest in decimal

n=number of compoundings per year

t=time in years

Given that;

t=4 years

A=$18000

P=?

r=0.08

n=2

Substitute values in the formula

[tex]A=P(1+\frac{r}{n} )^{nt} \\\\\\18000=P(1+\frac{0.08}{2} )^{2*4} \\\\\\18000=P(1+0.04)^8\\\\\\18000=P(1.04)^8\\\\\\18000=1.36856905041P\\[/tex]

Divide both sides by 1.36856905041 to remain with P

[tex]\frac{18000}{1.36856905041} =\frac{1.36856905041P}{1.36856905041}[/tex]

P=$13152.56

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