A Mutual Fund had a market value of $250,000 as of January 1, 2014. The following deposits were made to the Fund as follows:
1-January 15, 2014...........$10,000
2-Match 24, 2014............. $5,000
3-May 5, 2014.................. $3,000
4-July 18, 2014.................$6,000
5-Sept. 26, 2014...............$2,000
6-Nov. 3, 2014..................$4,000
At the end of December 31, 2014, the market value of the Fund was calculated to be
$316,009.98. What was the yield of this Fund as of January 1, 2015?
This kind of calculation is rather uncoventional in the sense that the deposits made are at irregular intervals. The only solution is rather laborious, in the sense that you have to figure out the exact number of days from the deposit day to the year end of 2014.
Once that is done, then it is simply a matter of projecting their FV to Dec.31, 2014. But, since we don't know the yield, a method of "iteration" has to be used, until we get as close as possible to the market value of the Fund at Dec. 31, 2014. So, we have:
January 1, 2014.............$250,000 on deposit for 365 days
1-January 15, 2014...........$10,000 '''''''''''''''''''''''''''''' 351 '''
2-Match 24, 2014............. $5,000 '''''''''''''''''''''''''''''' 283 '''
3-May 5, 2014.................. $3,000 ''''''''''''''''''''''''''''''' 241 ''
4-July 18, 2014.................$6,000 ''''''''''''''''''''''''''''''' 167 ''
5-Sept. 26, 2014...............$2,000 '''''''''''''''''''''''''''''''' 97 ''
6-Nov. 3, 2014..................$4,000 '''''''''''''''''''''''''''''''' 59 ''
By using the FV formula: FV=PV(1 + i)^n for the above 7 deposits, using iteration for "i", it will be found, after several attempts, that the rate converges to about 12.56%(rounded). This is the yield of the Fund compounded DAILY. Then, we simply annualize it to get: 13.38%(rounded), which is the yield on this Fund for 2014.