Question

For the cash flow given below, determine the value of A that will make the future worth in year 8 equal to 40000 TL at an interest rate of 10% per year. (Note: you should use at least one A formulation in the solution (A/P , P/A, A/F or F/A). ). (25 pts)( Year 0, 1, 2, 3, 5 Cash Flow, TL 0, 1250, 1250, 1250, 1250+2A)

Answer 1

Year	Cash flow (TL)
0	0
1	1250
2	1250
3	1250
4	1250
5	1250+2A

Interest rate = 10% per year

Required future worth at the end of year 8 = 40,000 TL

Future worth of the given cash at the end of year 8 = 1250(P/A, 10%, 5)(F/P, 10%, 8) + 2A*(F/P, 10%, 3)

Explanation: The annual cash flow of $1250 is discounted to present worth and the PW is converted to the future worth, while the cash flow of 2A is directly converted to the future worth)

From the compound interest factor table, we obtain

(P/A, 10%, 5) = 3.791

(F/P, 10%, 8) = 2.144

(F/P, 10%, 3) = 1.331

1250(P/A, 10%, 5)(F/P, 10%, 8) + 2A*(F/P, 10%, 3) = 40,000

=> 1250*3.791*2.144 + 2A * 1.331 = 40,000

=> 10,160 + 2.662A = 40,000

=> A = (40,000 - 10,160)/2.662

A = 11,210 TL