Au investor deposits 50 ill an investment account on January

Au investor deposits 50 ill an investment account on January 1. The following summarizes the activity in the account during the year: On June 30, the value of the account is 1J17.50. On December 31, the value of the account is X. Using the time-weighted method, the equivalent annual effective yield during the first G months is equal to the (time-weighted) annual effective yield during the entire 1-year period. Calculate X.

Solution

Answer:

                   X = 236.25

Explaination:

The Investor Deposit 50 in an investment account on January 1.

On June 30, the Value of the account is 157.50. On December 31, the value of the account is X

According to the time-weighted method

                The 6-month yield = (40/50)(80/60)(157.50/160) – 1

                                                       = 5%

                Annual equivalent = (1.05)² – 1

                                                    = 10.25%

                1-year yield = (40/50)(80/60)(175/160)(X/250) – 1 = 0.1025

                                           X(0.004667) = 1.1025

                                                                 X = 236.25

Therefore on December 31^st the value of account (X) = 236.25