$$Long$-$term investment$$ decision, payback method Personal Finance Problem$$Bill Williams has the opportunity to invest in project A that costs $ $7$ comma $200$ today and promises to pay $ $2$ comma $200,$ $ $2$ comma $500,$ $ $2$ comma $500,$ $ $2$ comma $100$ and $ $1$ comma $900$ over the next $5$ years. $$ Or$,$ Bill can invest $ $7$ comma $200$ in project B that promises to pay $ $1$ comma $600,$ $ $1$ comma $600,$ $ $1$ comma $600,$ $ $3$ comma $400$ and $ $4$ comma $000$ over the next $5$ years.$($Hint: For mixed stream cash$$ inflows, calculate cumulative cash inflows on a$$ year$-$to$-$year basis until the initial investment is recovered.$)$

a$.$How long will it take for Bill to recoup his initial investment in project$$ A$?$

b$.$How long will it take for Bill to recoup his initial investment in project$$ B$?$

c$.$Using the payback$$ period, which project should Bill$$ choose?

d$.$Do you see any problems with his$$ choice?

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Part $1$

a$.$For Bill to recoup his initial investment in project$$ A$,$ it will take

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enter your response here years.$($Round to two decimal$$ places.$)$