Bart and Lisa each borrow $17,000 from their father Homer. Homer and Lisa have agreed that...

Bart and Lisa each borrow $17,000 from their father Homer. Homer and Lisa have agreed that she will repay her loan in full by paying $4,000 in two years and $15,000 in four years. Bart prefers to make the same payment of $

X in two and four years to fully repay his loan. Determine X so that Bart and Lisa have the same effective interest rate (Round your answer to the nearest cent.)

Expert Solution

Ans:

Please find attached answer in excel sheet. For any query please ask in comment box.

Year	Cash flow
0	-17000
1	0
2	4000
3	0
4	15000
IRR	3.1660%

So effective rate of interest is 3.1660%


Now Bart has to pay equal amount in year 2 and 4 to repay with same effective rate of interest

Installment of Bart	x(pv factor of 3.1660% for 2 years) + x(pv factor of 3.1660% for 4 years) = 17,000

Now Solving for X we have	x(1/1.031660^2+1/1.031660^4) = 17000

X =	9328.628025

Formulas are as below:

Year	Cash flow
0	-17000
1	0
2	4000
3	0
4	15000
IRR	=IRR(B2:B6)

So effective rate of interest is 3.1660%


Now Bart has to pay equal amount in year 2 and 4 to repay with same effective rate of interest

Installment of Bart	x(pv factor of 3.1660% for 2 years) + x(pv factor of 3.1660% for 4 years) = 17,000

Now Solving for X we have	x(1/1.031660^2+1/1.031660^4) = 17000

X =	=17000/1.82234729

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