What is the present value of a series of 41 quarterly deposits (starting at quarter 1)...

What is the present value of a series of 41 quarterly deposits (starting at quarter 1) when the first deposit is $500 and the deposits increase by $31 each quarter starting with the second quarter? The nominal annual interest rate is 10% and is compounded weekly.

Expert Solution

Weekly interest rate=10%/52=0.1923% (Assunimg 1year=52 week)

Quarterly effective interest rate= (1+0.1923%)^13-1=2.53% (1 quarter=13 weeks)

Quarter	Deposit	Present Value (Deposit/1.0253^Quarter)
1	500.0	487.7
2	531.0	505.1
3	562.0	521.4
4	593.0	536.6
5	624.0	550.7
6	655.0	563.8
7	686.0	575.9
8	717.0	587.1
9	748.0	597.4
10	779.0	606.8
11	810.0	615.4
12	841.0	623.1
13	872.0	630.2
14	903.0	636.5
15	934.0	642.1
16	965.0	647.0
17	996.0	651.3
18	1,027.0	655.0
19	1,058.0	658.1
20	1,089.0	660.7
21	1,120.0	662.7
22	1,151.0	664.3
23	1,182.0	665.3
24	1,213.0	665.9
25	1,244.0	666.1
26	1,275.0	665.9
27	1,306.0	665.2
28	1,337.0	664.2
29	1,368.0	662.8
30	1,399.0	661.1
31	1,430.0	659.1
32	1,461.0	656.8
33	1,492.0	654.2
34	1,523.0	651.3
35	1,554.0	648.1
36	1,585.0	644.8
37	1,616.0	641.1
38	1,647.0	637.3
39	1,678.0	633.3
40	1,709.0	629.1
41	1,740.0	624.7
	Present Value (Total)	25,675.3

Hence, present value is $25675.3

jeff jeffy answered 3 months ago

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