Question

You plan to start saving money by depositing $500 into a saving account one year from now. You estimate that the deposits will increase by $100 per year for 9 years thereafter. What would be the present worth of the investments if the interest rate is 5% per year? What would be the equivalent uniform annual series? Also,draw a properly labeled Cash Flow Diagram for this question.

Answer 1

Cash Flow diagram -

Interest Rate = 9%

PV of a cash flow = Cash Flow * PV Factor, where PV Factor = 1/(1+r)ⁿ

Time	Cash Flow	PV Factor	PV
1	500	0.95	476.19
2	600	0.91	544.22
3	700	0.86	604.69
4	800	0.82	658.16
5	900	0.78	705.17
6	1000	0.75	746.22
7	1100	0.71	781.75
8	1200	0.68	812.21
9	1300	0.64	837.99
10	1400	0.61	859.48
		NPV	7026.07

Hence, NPV = $7026.07

Let the uniform series have cash flow X each period

Hence, PV = X [1 - (1+r)^-n]/r = X (1-1.05^-10)/0.05

This is equal to NPV we found earlier

=> X (1-1.05^-10)/0.05 = 5646.11

=> X = $731.20