Question

QUESTION 1 Consider the following cash flow diagrams. In these diagrams the present value (P) and the future value (F) are economically equivalent to the uniform series of payments (A) at a discount rate of 8% per period. Is the value of P larger than F equal to or less than F? P is larger than F P equals F P is less than F

Consider the following cash flow diagrams. In these diagrams the present value (P) and the future value (F) are economically equivalent to the uniform series of payments (A) at a discount rate of 8% per period. Is the value of P larger than F, equal to F, or less than F?

Answer 1

Future value is always larger than present value as interest is added in future value. Now, let's consider the cash flow as $ 1,000 per year and calculate pv and Fv of annuities. Calculation of present value (pv): - pv = c times [1 minus (1 + v)^minus n/r] c = cash flow per period = $ 1,000 r = Rate per period = 8% = 0.08 n = Number of periods = 7. Pv = $ 1,000 times [1 minus (0.1 + 0.08)^minus 7/0.08] = $ 1,000 times [1 minus (1.08)^minus 7/0.08] = $1,000 times [(1 minus 0.58349)/0.08] = $ 1,000 times [0.41651/0.08] = $ 1,000 times 5.20637 = $ 5,206.37 calculation of Future value (Fv): - Fv = c times [(1 + r)^n minus 1/r] \r\n = $ 1,000 times [(1 + 0.08)^7 minus 1/0.08] = $ 1,000 times [(1.08)^7 minus 1/0.08] = $ 1,000 times [1,713824 minus 1/0.08]