Question

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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.

Solutions

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


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