Question

Stan elects to receive his retirement benefit over 20 years at the rate of 2000 per month beginning one month from now.The monthly benefit increases by 5% each year.At a nominal interest rate of 6% convertible monthly, calculate the present value of the retirement benefit.

Answer 1

interest rate per month = 6%/12 = 0.5%

Year (n)	Amount/month	PV at n	PV at t = 0
1	2,000.00	23,237.86	23,237.86
2	2,100.00	24,399.76	22,982.26
3	2,205.00	25,619.75	22,729.47
4	2,315.25	26,900.73	22,479.46
5	2,431.01	28,245.77	22,232.20
6	2,552.56	29,658.06	21,987.66
7	2,680.19	31,140.96	21,745.81
8	2,814.20	32,698.01	21,506.62
9	2,954.91	34,332.91	21,270.06
10	3,102.66	36,049.55	21,036.10
11	3,257.79	37,852.03	20,804.72
12	3,420.68	39,744.63	20,575.88
13	3,591.71	41,731.87	20,349.55
14	3,771.30	43,818.46	20,125.72
15	3,959.86	46,009.38	19,904.35
16	4,157.86	48,309.85	19,685.42
17	4,365.75	50,725.34	19,468.89
18	4,584.04	53,261.61	19,254.74
19	4,813.24	55,924.69	19,042.95
20	5,053.90	58,720.93	18,833.49
		PV of benefits	4,19,253.21

Steps:

1. Calculate the monthly benefit per year since it is increasing by 5% every year - 2000*(1+5%) and so on

2. For every year, calculate the PV of that year's monthly benefits, at the beginning of that year by using the PV formula -

For example, for Year 2, PMT = 2,100; i = 0.5%; N = 12, solve for PV. PV = 24,399.76

3. For each calculated PV at t = n, use this PV as FV and discount it to t = 0 (ie at present) -

For example, the PV at the beginning of year 20 (ie end of year 19) will be discounted back 19 years to get to t = 0. FV = 58,720.93; i = 0.5%, n = 19*12 = 228, solve for PV. PV = 18,833.49

4. The PV of the retirement benefits will be the sum of all PVs calculated in step 3.