Question

A fund earned a net investment income (i.e. Ending Balance Starting Balance + Deposits/Withdrawals)) of 9200 during 1999. The beginning and ending balances of the fund were 100000 and 129200, respectively. A deposit was made at time K during the year. No other deposits or withdraws were made. The fund earned 8% in 1999 using the dollar-weighted method. Determine then date corresponding to time K
(a) April 1 (b) May 1 (c) July 1 (d) Sept. 1 (e) Oct. 1
Answer:________

Answer 1

Answer:

k = April 1 ( A )

Explanation:

Given data :

net investment income : $9200

Beginning balance = $100000

ending balance = $129200

deposit made

no withdrawals

interest earned = 8%

net investment ( $9200) = [ending balance - (starting balance + deposits/withdrawals )]

9200 = 129200 - 100000 - deposits

deposit = 129200 -100000 - 9200 = 20000

8% interest was earned on starting balance

= 8% of $100000 = $8000

interest earned on the deposit made = net income - interest earned on beginning balance = 9200 - 8000 = $1200

using the dollar-weighted method

assuming the deposit was made for Y months

interest earned on deposit = deposit * interest rate * (y/12)

                    1200 = 20000 * 8% * ( y /12 )

                     hence ( y/12) =  0.75 hence y = 9 months from December 31

which makes K = April 1