Question

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.​

Answer 1

$29364.95

Explanation:

The formula to apply is;

`A=P(1+(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+(r)/(n) )^(nt) \\\\\\55000=P(1+(0.08)/(2) )^(8*2) \\\\\\55000=P(1+0.04)^(16) \\\\\\55000=P(1.04)^(16) \\\\\\55000=1.8729P\\\\\\(55000)/(1.8729) =(1.8729P)/(1.8729) \\\\\\29364.95=P`

Checking the answer

`A=P(1+(r)/(n) )^(nt) \\\\\\A=29364.95(1+(0.08)/(2) )^(16) \\\\\\A=29364.95(1.04)^(16) \\\\\\A=55000`