Paul Palumbo assumes that he will need to have a newroof put on his house in four years. He estimates thatthe roof will cost him $18,000 at that time. Whatamount of money should Paul invest today at 8%,compounded semiannually, to be able to pay for theroof?O $13,152.60$24,634.80$15,431.40O $ 9,725.40O none of the above​

Answer:$13,52.60Step-by-step explanation:The formula to apply is [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]whereA= amount of money at the endP=the amount of money to invest, principalr=rate of interest in decimaln=number of compoundings per yeart=time in yearsGiven that;t=4 yearsA=$18000P=?r=0.08n=2Substitute values in the formula[tex]A=P(1+\frac{r}{n} )^{nt} \\\\\\18000=P(1+\frac{0.08}{2} )^{2*4} \\\\\\18000=P(1+0.04)^8\\\\\\18000=P(1.04)^8\\\\\\18000=1.36856905041P\\[/tex]Divide both sides by 1.36856905041 to remain with P[tex]\frac{18000}{1.36856905041} =\frac{1.36856905041P}{1.36856905041}[/tex]P=$13152.56