Question

Jim borrowed 10,000 from Bank X at an annual effective rate of 8%. He agreed to repay the bank with 5 level annual installments at the end of each year. At the same time, he also borrowed 15,000 from bank Y at an annual effective rate of 7.5%. He agreed to pay the bank this loan with 5 level annual installments at the end of each year. He lent the 25,000 to Wayne immediate in exchange for 4 annual level repayments at the end of each year, at an annual effective rate of 8.5%. Jim can only reinvest the proceeds at an annual effective rate of 6%. Immediately after repaying the loans to the banks in full, determine how much Jim has left.

Answer 1

$373.43

Step-by-step explanation:

the cash outflows associated to the first loan are 5 level payments of $2,504.56 each (= $10,000 / 3.992717 PV annuity factor, 8%, 5 periods).

the cash outflows associated to the second loan are 5 level payments of $3,707.47 each (= $15,000 / 4.048857 PV annuity factor, 7.5%, 5 periods).

total cash outflows associated to both loans = $6,212.03

inflows associated with investment are 4 level payments of $7,632.20 each (= $25,000 / 3.275596 PV annuity factor, 8.5%, 4 periods).

net cash flow year 1 = $7,632.20 - $6,212.03 = $1,420.17

net cash flow year 2 = $7,632.20 - $6,212.03 + ($1,420.17 x 1.06) = $2,925.55

net cash flow year 3 = $7,632.20 - $6,212.03 + ($2,925.55 x 1.06) = $4,521.25

net cash flow year 4 = $7,632.20 - $6,212.03 + ($4,521.25 x 1.06) = $6,212.70

net cash flow year 5 = ($6,212.70 x 1.06) - $6,212.03 = $373.43