Question

A 20 year annuity pays 1600 per month at the end of each month. if the discount rate is 10% compounded monthly for the first nine years and 8% compounded monthly thereafter, what is the present value of the annuity?

Answer 1

The answer is $182,033.84

Calculations and explanations:

From months 1 - 108 (i.e. first 9 years) the 1+r = 1+(10%/12) = 1.00833

From month 109 onwards 1+r = 1+(8%/12) = 1.00667

We can compute PVIF using the formula: PVIF = 1/(1+r)^n

Month	Payment	1+r	PVIF	PV = $1600*PVIF
1	1,600.00	1.008333	0.9917	1,586.78
2			0.9835	1,573.66
3			0.9754	1,560.66
4			0.9673	1,547.76
5			0.9594	1,534.97
6			0.9514	1,522.28
7			0.9436	1,509.70
8			0.9358	1,497.22
9			0.9280	1,484.85
10			0.9204	1,472.58
108			0.4081	652.94
109		1.00667	0.4847	775.50
110			0.4815	770.36
111			0.4783	765.26
112			0.4751	760.19
113			0.4720	755.16
239			0.2043	326.92
240			0.2030	324.75
			Total	182,033.84