Question

An investor deposits 50 in an investment account on January 1. The following summarizes the activity in the account during the year: DateValue Immediately Before DepositDeposit March 154020 June 18080 October 117575 On June 30, the value of the account is 157.50. On December 31, the value of the account is X. Using the time-weighted method, the equivalent annual effective yield during the first 6 months is equal to the (time-weighted) annual effective yield during the entire 1-year period. Calculate X.

Answer 1

236.25

Step-by-step explanation:

Calculation to determine X

First step is to calculate the 6 months Yield

6 month Yield=(40/40+20) (80/40+20) (157.60/80+80)+1)

6 month Yield=(40/60) (80/60) (157.60/160)-1

6 month Yield=5%

Second step is to calculate the Annual equivalent

Annual equivalent=(1.05)^2-1

Annual equivalent=10.25%

Third step is to calculate the 1 year yield

1 year yield=(40/50) (80/40+20) (175/80+80) (x/175+75)

1 year yield=(40/50) (80/60) (175/160) (x/250)-1

1 year yield=0.1025

Now Let calculate X

x(0.004667)=1+.1025

x(0.004667)=1.1025

x=1.1025/0.004667

x=236.25

Therefore X is 236.25