The following deposits were made into a balanced mutual fund in 2015. The number of days is the length of time each deposit earned interest:
$30,000 on deposit for 300 days.
$10,000 on deposit for 257 days.
$25,000 on deposit for 179 days.
$15,000 on deposit for 143 days
$20,000 on deposit for 107 days
These deposits totaling $100,000 were worth $112,500 on Dec,31, 2015. What was the overall yield on this mutual fund for 2015?. Thank you for any help.
+118608 The following deposits were made into a balanced mutual fund in 2015. The number of days is the length of time each deposit earned interest:
$30,000 on deposit for 300 days.
$10,000 on deposit for 257 days.
$25,000 on deposit for 179 days.
$15,000 on deposit for 143 days
$20,000 on deposit for 107 days
These deposits totaling $100,000 were worth $112,500 on Dec,31, 2015. What was the overall yield on this mutual fund for 2015?. Thank you for any help.
I have assumed that the interested is calculated and added daily.
I have let R = 1+ the daily interest rate.
\(112,500=30000R^{300}+10000R^{257}+25000R^{179}+15000R^{143}+20000R^{107}\\ 11.25=3R^{300}+1R^{257}+2.5R^{179}+1.5R^{143}+2R^{107}\\ \)
Now I have no idea how to do this so I entered it into Wolfram|Alpha
R = 1.00057
The daily interest rate is 0.00057 = 0.057%
You could say that the nominal yearly rate is 0.057*365.25 = 20.81925 %
But the acurate yearly rate - if the interest was calculated and added year is
1+yearly rate = 1.00057^365.25 = 1.2313771628891921 = approx 23.14%
These types of deposits are very common in the business world, where small and large businesses deposit regular or irregular amounts of money into mutual funds or many other investment accounts.
The purpose, in this example, is to find the interest rate that these funds earned in 2015. This interest rate is called IRR, or Internal Rate of Return.
Many softwares are available to calculate such returns, including many spreadsheets such as Excel to calculate these returns. I happened to have software programmed into my computer to do these calculation very rapidly.
All these softwares do the same thing, which is to find the PV of all these payments which will equate them to the final market value of the fund, which in this case is $112,500. So, they use iteration to find a couple of interest rates, and then use interpolation between them to arrive at actual IRR. This is what Wolfram/Alpha does.
Now, entering these amounts into my computer, it comes out with a daily rate of=.00057492740959, which is essentially the same as Melody found using Wolfram/Alpha engine. The custom, in the business world, is to raise this number to the power of 365 days to find the Effective IRR.
So, 1.00057492740959^365=23.34%, which is basically the same as Melody found.
