You have just received an inheritance of $28,000 and would like to invest it into an account. The bank offers two investment pla
ns, one for 4 years at 5.8% compounded annually and another for 3 years at 7.083% compounded annually. You want to make equal annual withdrawals from the account over the life time of the loan. Which investment will yield the highest return over the duration of the loan, given that the account will be zeroed out by the end of that period? a.
3 year account; $32,056.89
c.
3 year account; $24,130.77
b.
4 year account; $42,742.52
d.
4 year account; $32,174.36
First we need to calculate annual withdrawal of each investment The formula of the present value of an annuity ordinary is Pv=pmt [(1-(1+r)^(-n))÷(r)] Pv present value 28000 PMT annual withdrawal. ? R interest rate N time in years Solve the formula for PMT PMT=pv÷[(1-(1+r)^(-n))÷(r)]
Now solve for the first investment PMT=28,000÷((1−(1+0.058)^(−4)) ÷(0.058))=8,043.59 The return of this investment is 8,043.59×4years=32,174.36
Solve for the second investment PMT=28,000÷((1−(1+0.07083)^( −3))÷(0.07083))=10,685.63 The return of this investment is 10,685.63×3years=32,056.89
So from the return of the first investment and the second investment as you can see the first offer is the yield the highest return with the amount of 32,174.36
