Question

On January 1, 1999, Luciano deposits 90 into an investment account. On April 1, 1999, when the amount in Luciano’s account is equal to X, a withdrawal of W is made. No further deposits or withdrawals are made to Luciano’s account for the remainder of the year. On December 31, 1999, the amount in Luciano’s account is 85. The dollar-weighted return over the 1-year period is 20%. The time-weighted return over the 1-year period is 16%. Calculate X.

Answer 1

Answer:

X = 107.63

Explanation:

From the given information:

The amount of interest earned on this account will be:

= 85 + W - 90

= W - 5

However; the dollar weight return rate is:

$\dfrac{(W-5)}{(90 - \dfrac{3}{4*W})} = 0.2$

$\dfrac{(W-5)}{(90 - 0.75W})} = 0.2$

W - 5 = 0.2(90 - 0.75W)

W - 5 = 18 - 0.15 W

W + 0.15 W = 18 + 5

1.15 W = 23

W = 23/1.15

W = 20

The time weighted return rate can be computed as:

$0.16 = \dfrac{X}{90} \times \dfrac{85}{X-20} -1$

$1+0.16 = \dfrac{X}{90} \times \dfrac{85}{X-20}$

$1.16 = \dfrac{X}{90} \times \dfrac{85}{X-20}$

1.16×((90)(X-20)) = 85X

1.16 × (90X - 1800) = 85X

104.4X - 2088 = 85 X

104.4X - 85 X = 2088

19.4X = 2088

X = 2088/19.4

X = 107.628866

X = 107.63