Question

Suppose that an annuity will provide for 20 annual payments of 1340 dollars, with the first payment coming 9 years from now. If the nominal rate of interest is 9.6 percent convertible monthly, what is the present value of the annuity?

Answer 1

Rate is quoted yearly 9.6 %, so monthly rate will be 9.6/12 = 0.8%

We need to compound by 0.8% per month.

First payment will be received after 9 years means 9*12=108 months

Thereafter annually we will receive installment of $1340, means 108+12 = 120 months, 132 months and so on.

Present value is calculated by : - FV/(1+r)^t

Here FV is 1340, r is 0.8% and t is 108, solving it comes to $566.71, its the first installment

For second installment FV is 1340, r is 0.8% and t is 120, solving it comes to $515.04, its second installment

doing this till all 20 installments and accumulating its balance will be our Present Value.

I have done that in excel, here is the table below :-

Installment	FV	Base	Rate	Rate	Period	Factor	PV
1	1340	1	0.008	1.008	108	2.36	566.7184
2	1340	1	0.008	1.008	120	2.60	515.04
3	1340	1	0.008	1.008	132	2.86	468.074
4	1340	1	0.008	1.008	144	3.15	425.3909
5	1340	1	0.008	1.008	156	3.47	386.5999
6	1340	1	0.008	1.008	168	3.81	351.3463
7	1340	1	0.008	1.008	180	4.20	319.3074
8	1340	1	0.008	1.008	192	4.62	290.1901
9	1340	1	0.008	1.008	204	5.08	263.728
10	1340	1	0.008	1.008	216	5.59	239.6789
11	1340	1	0.008	1.008	228	6.15	217.8229
12	1340	1	0.008	1.008	240	6.77	197.9598
13	1340	1	0.008	1.008	252	7.45	179.9081
14	1340	1	0.008	1.008	264	8.20	163.5025
15	1340	1	0.008	1.008	276	9.02	148.5929
16	1340	1	0.008	1.008	288	9.92	135.0428
17	1340	1	0.008	1.008	300	10.92	122.7284
18	1340	1	0.008	1.008	312	12.01	111.537
19	1340	1	0.008	1.008	324	13.22	101.366
20	1340	1	0.008	1.008	336	14.55	92.12256
							5296.657

Present Value of annuity is $5296.65