In: Finance
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.
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