Question

4. John Payer, owner of Payer's Garage, estimates he will need $55,000 for

Answer 1

Answer:

$29364.95

Step-by-step explanation:

The formula to apply is;

$A=P(1+\frac{r}{n} )^{nt}$

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;

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

Checking the answer

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