The sum should be invested today at 6%, compounded semiannually, to yield $26,000 is $17,189.06 .
Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.
Formula of compound interest :
[tex]A = P (1+\frac{r}{100} )^{t}[/tex]
where,
A = final amount
P = initial amount
r = rate per annum
t = time in years
According to the question
Southwest Dry Cleaners need new equipment in (t)7 years.
Equipment cost (A)= $26,000.
He invest today at = 6% compounded semiannually
As rate is compounded semiannually = 6%
R = 6/2
R = 3%
and time = 7 * 2 = 14
Now ,
Substituting values in Formula of compound interest
[tex]A = P (1+\frac{r}{100} )^{t}[/tex]
[tex]26000 = P (1+\frac{3}{100} )^{14}[/tex]
[tex]26000 = P (1.03 )^{14}[/tex]
26000 = 1.5125 * P
P = 17,189.06
Hence, The sum should be invested today at 6%, compounded semiannually, to yield $26,000 is $17,189.06 .
To know more about compound interest here:
https://brainly.com/question/14295570
#SPJ2
