Question

Assume the appropriate discount rate is 7%. You will receive a payment every year for the next 14 years, which will grow at 3% annually. The amount of the first payment will be $5,000. What is the current value of this series of payments?

Answer 1

Questions ask you to calculate the current value of the series payment i.e. you need to calculate the Present value of all the payments you are going to receive in next 14 years.

Given Information: 1st Payment wiil be $5000 and at the end of year., Discount rate = 7% , Payment grow 3% annually.

Step 1: You need to calculate the Payments you are going to receive. Payment grow 3% every year.

Step 2 : After knowing the payments you need to discount that payments with the 7% rate to calculate the present value. PV factors are easily available with PV factor table or cab easily calculate as 100 / (1+rate) power to corresponding year.

Step 3: Add all the payments to get the current value.

Following Sheet will elaborate the process:

Year End		Payments	Present Value factor @ 7%	Present Value
0	0	0.00	1.00000	0.00
1	5000	5000.00	0.93458	4672.90
2	5000(1.03)	5150.00	0.87344	4498.21
3	5000(1.03)2	5304.50	0.81630	4330.05
4	5000(1.03)3	5463.64	0.76290	4168.18
5	5000(1.03)4	5627.54	0.71299	4012.36
6	5000(1.03)5	5796.37	0.66634	3862.37
7	5000(1.03)6	5970.26	0.62275	3717.98
8	5000(1.03)7	6149.37	0.58201	3578.99
9	5000(1.03)8	6333.85	0.54393	3445.19
10	5000(1.03)9	6523.87	0.50835	3316.40
11	5000(1.03)10	6719.58	0.47509	3192.42
12	5000(1.03)11	6921.17	0.44401	3073.08
13	5000(1.03)12	7128.80	0.41496	2958.20
14	5000(1.03)13	7342.67	0.38782	2847.61
			Total	51673.95

Current Value of payments = 51674.