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#1
06-25-2018, 11:04 AM
 actsci123451 SOA Join Date: Feb 2018 Posts: 11
Question on Interest

On January 1, an investment fund was opened with an initial balance of 5000. Just after the balance grew to 5200 on July 1, an additional 2600 was deposited.The annual effective yield rate for this fund was 9.00% over the calendar year.

Calculate the time-weighted rate of return for the year.

SOA calculates the ending balance as 5000(1.09) + 2600(1.09)^0.5 = 8164.48

I did the following and cant understand why it doesn't give the same answer.
5200(1.09)^0.5 + 2600(1.09)^0.5 = 8143.43

Can someone please explain what I am doing wrong?
#2
06-25-2018, 11:33 AM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 6,045

What rate was earned during the first 6 months? Was it 9%? The last six months need to make it 9% over the year.
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#3
06-25-2018, 11:44 AM
 therealsylvos Member CAS Join Date: Mar 2014 Posts: 17,127

Quote:
 Originally Posted by Colymbosathon ecplecticos What rate was earned during the first 6 months? Was it 9%? The last six months need to make it 9% over the year.
This is what I was going to say, but it's a little weird isn't it?

If we ignore the \$2600 deposited, the ending balance is 5450. This means from July to January the fund needs earn 4.8%, but the SOA solution has the 2600 earning 4.4%. Presumably all money in the fund earns the same interest rate over a given time period.
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#4
06-25-2018, 05:37 PM
 Chuck Member SOA AAA Join Date: Oct 2001 Location: Illinois Posts: 4,604

yes, the SOA answer seems wrong to me too if i understand the terms used.

The 5,000 must accumulate to 5000*1.09 = 5450. That means it must have earned 5450/5200 during the 2nd half. Which should mean that the 2600 accumulates to 2600 * 5450/5200 = 2,725 for a total accumulation of 8,175 = 5450+2725. So the time-weighted return (if I am interpreting what that means correctly) is something north of 9%.
#5
06-26-2018, 08:46 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,416

The 9% is simply the solution of an equation. It doesn't imply that the rate was constant over the year. The fund earned 4% for the first half of the year and 8164.48.78/7800 - 1 for the second half of the year. With the larger amount invested for the second half of the year "dollar weighted" rate over the entire year was 9%.