Kathy has $50,000 to invest today and would like to determine whether it is realistic for her to achieve her goal of buying a home for $150,000 in 10 years with this investment. What return must she achieve in order to buy her home in 10 years?a) About 12%b) About 13%c) About 9%d) About 10%

Answer:a) About 12%Step-by-step explanation:We need to find the interest rate required to achieve her goal, so we will need to use the interest-compound formula:[tex]FV=PV(1+i)^{n}[/tex]Where:PV= Present Valuei= interest rateFV= Future Valuen= number of periodsreplacing the data provided:[tex]150.000=50.000(1+i)^{10}[/tex]solving for i:first, divide both sides by 50.000 to simplify the equation:[tex]3=(1+i)^{10}[/tex]Take [tex]10^{th}[/tex] roots of both sides:[tex]1+i=[/tex]±[tex]\sqrt[10]{3}[/tex]solve for i:[tex]i=[/tex]±[tex]\sqrt[10]{3} -1[/tex]We get two answers, but we look for a coherent value. So we take the positive one:[tex]i=11.6123174[/tex]≈12