Question

An annuity pays quarterly for 16 years at the beginning of each quarter. Payments during the first year are 250/quarter. Year 2 payments are each 105. The payments go up by 150 for each subsequent year but are level within each year. AEIR = 5%, please find the accumulated value of this annuity just prior to the payment at t=15.

	A.	79,798.78
	B.	72,848.29
	C.	The answer does not appear here
	D.	156,104.12
	E.	154,014.68

and this is the previous question

An annuity pays quarterly for 16 years at the beginning of each quarter. Payments during the first year are 250/quarter. Year 2 payments are each 105. The payments go up by 150 for each subsequent year but are level within each year. AEIR = 5%, eventually we would like to find the accumulated value of this annuity just prior to the payment at t=15.

What is the quarterly interest rate i 1/4?

	D.	.0122722355

Answer 1

The correct answer is the first option i.e. option A.   79,798.78

r = (1 + 5%)^1/4 - 1 = 0.012272234

Please see the table below. Please be guided by the header to understand the mathematics. The last row highlighted in yellow is your answer. Figures in parenthesis, if any, mean negative values. All financials are in $.

t	n = 60 - t	Cash flows, C	FV = C x (1 + r)^n
0	60	250	519.73
1	59	250	513.43
2	58	250	507.21
3	57	250	501.06
4	56	105	207.89
5	55	105	205.37
6	54	105	202.88
7	53	105	200.42
8	52	255	480.84
9	51	255	475.01
10	50	255	469.25
11	49	255	463.56
12	48	405	727.32
13	47	405	718.50
14	46	405	709.79
15	45	405	701.19
16	44	555	949.24
17	43	555	937.73
18	42	555	926.36
19	41	555	915.13
20	40	705	1,148.37
21	39	705	1,134.45
22	38	705	1,120.70
23	37	705	1,107.11
24	36	855	1,326.39
25	35	855	1,310.31
26	34	855	1,294.42
27	33	855	1,278.73
28	32	1005	1,484.84
29	31	1005	1,466.84
30	30	1005	1,449.06
31	29	1005	1,431.49
32	28	1155	1,625.20
33	27	1155	1,605.50
34	26	1155	1,586.03
35	25	1155	1,566.81
36	24	1305	1,748.82
37	23	1305	1,727.62
38	22	1305	1,706.68
39	21	1305	1,685.99
40	20	1455	1,856.99
41	19	1455	1,834.48
42	18	1455	1,812.24
43	17	1455	1,790.27
44	16	1605	1,950.89
45	15	1605	1,927.24
46	14	1605	1,903.87
47	13	1605	1,880.79
48	12	1755	2,031.63
49	11	1755	2,007.00
50	10	1755	1,982.67
51	9	1755	1,958.63
52	8	1905	2,100.26
53	7	1905	2,074.80
54	6	1905	2,049.65
55	5	1905	2,024.80
56	4	2055	2,157.75
57	3	2055	2,131.59
58	2	2055	2,105.75
59	1	2055	2,080.22
Total			79,798.78