Question

x=3000

P 1.2 = Calculate the present worth for the cash flows with different specified periodic interest rates. The cash flow diagram is given: Note that X is the last digit of your University ID and its in 1000. For example, if student ID is 3, the value of X is $ 3000. PE? 8% Comp annually 9% Compounded quarterly 12% compounded monthly $2000 + X $2000 + X $2000 + X

Answer 1

X = 3,000

Cash Flow = 5,000

Present value is calculated as: Cash Flow / [1 + (Rate of Interest / Compounding done in a year)]^^{Compounding done year an year * Year}]

Money withdrawn in year 2 at 8% compounded annually is $5,000. Its present value is [5,000 / (1 + 0.08)^²] = 4,286.694

Money withdrawn in year 4 at 9% compounded quarterly from year 2 to 4 and 8% compounded annually from year 0 to 2 is $5,000. Its present value is 5,000 / {[1 + 0.08]^² * [1 + (0.09 / 4)^⁸]} = 3,587.699

Money withdrawn in year 4 at 12% compounded monthly from year 4 to 6 and 9% compounded quarterly from year 2 to 4 and 8% compounded annually from year 0 to 2 is $5,000. Its present value is 5,000 / {[1 + 0.08]^² * [1 + (0.09 / 4)^⁸] * [1 + (0.12 / 12)]^²⁴} = 2,825.55

Sum of present value = 4,286.694 + 3,587.699 + 2,825.55 = 10,699.94 or 10,700