Jim should invest $6,260.47 of amount today at 4% compounded quarterly to be able to pay for the roof.
Compound interest, also known as interest on principal with interest, is the practice of adding interest to the principal amount of a loan or deposit.
A = accumulated amount $10,700
P = original amount deposited
r = rate 4%
=0.04
n = times it compounds per year 4
quarterly
t = 9 years
A = P[tex](1+\frac{r}{n} )^{nt}[/tex]
10700 = [tex]P(1+\frac{0.04}{9}) ^{4*9}[/tex]
10700 = P [tex](1.015) ^{36}[/tex]
P = [tex]\frac{10700}{(1.015) ^{36} }[/tex]
= $6,260.47
Hence, Jim should invest $6,260.47 of amount today at 4% compounded quarterly to be able to pay for the roof.
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