Question

Problem 4-97 (algorithmic) : Question Help Determine the present equivalent value of the cash-flow diagram shown below when the annual interest rate, is, varies as indicated. II $2,000 - L ---- P= ? $2,000 $1,000 $1,000 11 = 15% † in = 6% iz = 15% 14 = 10% 1 15 = 10% 1 3 4 Years im on TS 16 = 6% 5 The present equivalent value is $ 4617.5. (Round to the nearest cent.)

Answer 1

Present value is calculated as P / (1 + r)n

where, P is amount being able to withdraw after n year and r is rate of interest.

Present value of 1,000 able to withdraw after 1 year = [1,000 / (1 + 0.15)] = 869.56

Present value of 2,000 able to withdraw after 2 year = {2,000 / [(1 + 0.16) (1 + 0.15)]} = 1,640.68

Present value of 1,000 able to withdraw after 4 year = {1,000 / [(1 + 0.1) (1 + 0.15) (1 + 0.06) (1 + 0.15)]} = 648.49

Present value of 2,000 able to withdraw after 6 year = {2,000 / [(1 + 0.06) (1+ 0.1) (1 + 0.1) (1 + 0.15) (1 + 0.06) (1 + 0.15)]} = 1,112.33

Present value = 869.56 + 1,640.68 + 684.49 + 1,112.33 = 4,307.06