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4. John Payer, owner of Payer's Garage, estimates he will need $55,000 for
new equipment in 8 years. John decided he would put aside the money now
so that in 8 years the $55,000 will be available. His bank offers him 8%
interest compounded semiannually. How much will John invest today so his
account will have $55,000 in 8 years? Check your answer.​

Respuesta :

lucic

Answer:

$29364.95

Step-by-step explanation:

The formula to apply is;

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

where ;

A=amount at the end

P=principal amount

r=rate of interest as a decimal

n=number of compoundings a year

t=total number of years

Given in the question

A=$55000

t=8 years

n=2

r=0.08

P=?

Substitute the values in the equation;

[tex]A=P(1+\frac{r}{n} )^{nt} \\\\\\55000=P(1+\frac{0.08}{2} )^{8*2} \\\\\\55000=P(1+0.04)^{16} \\\\\\55000=P(1.04)^{16} \\\\\\55000=1.8729P\\\\\\\frac{55000}{1.8729} =\frac{1.8729P}{1.8729} \\\\\\29364.95=P[/tex]

Checking the answer

[tex]A=P(1+\frac{r}{n} )^{nt} \\\\\\A=29364.95(1+\frac{0.08}{2} )^{16} \\\\\\A=29364.95(1.04)^{16} \\\\\\A=55000[/tex]

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