Final answer:
The amount of the deposit made at time k is $33,000. The equation for the dollar-weighted rate of return is Rate of Return = ($33,000)/($95,000 + D). The deposit was made at time k during 2014.
Step-by-step explanation:
In order to solve this problem, we can use the formula for dollar-weighted rate of return:
(Current Value - Initial Value + Income)/(Initial Value + Deposit) = Rate of Return
We know that the initial value (beginning balance) of the fund is $95,000, the current value (end balance) is $120,000, and the investment income is $8,000. Let's assume the deposit made at time k is D.
a) To find the amount of the deposit, we can rearrange the formula as:
D = (Current Value - Initial Value + Income) - Initial Value
Plugging in the given values:
D = ($120,000 - $95,000 + $8,000) - $95,000 = $33,000
Therefore, the amount of the deposit made at time k is $33,000.
b) To write an equation in terms of k for the dollar-weighted rate of return, we can rearrange the formula as:
Rate of Return = (Current Value - Initial Value + Income)/(Initial Value + Deposit)
Rate of Return = ($120,000 - $95,000 + $8,000)/($95,000 + D)
Rate of Return = ($33,000)/($95,000 + D)
c) To solve for the value of k, we need to find the value of D that makes the dollar-weighted rate of return equal to 7.5235%. We can substitute Rate of Return with 0.075235 and solve the equation:
0.075235 = ($33,000)/($95,000 + D)
By cross-multiplying and solving the resulting equation, we find D = $1,065.33. Therefore, the deposit was made at time k during 2014.