Helene Gauthier inverted $15,000 on January 1 in a partnership

Given data

The investment on the January 1 is, E1= $15000.E1= $15000.

The withdraw on the June 1 is, W1=$1500.W1=$1500.

The withdraw on the August 1 is, W2=$1500.W2=$1500.

The reinvestment on the November 1 is, E2=$4000.E2=$4000.

The expression of the average monthly investment balance is,

I=E1T1+(E1−W1)T2+(E1−W1−W2)T3+(E1−W1−W2+E2)T4T1+T2+T3+T4I=E1T1+(E1−W1)T2+(E1−W1−W2)T3+(E1−W1−W2+E2)T4T1+T2+T3+T4

Here, T1T1 is the time period for the amount between 1 January to 31 May, T2T2 is time period for the amount between 1 June to 31 July, T3T3 time period for the amount between 1 August to 31 October, T4T4 is time period for the amount between 1 November to 31 December.

Substitute the given values,

I=( $15000)(5)+( $15000−$2000)(2)+( $15000−$2000−$1500)(3)+( $15000−$2000− $1500+$4000)(2)5+3+2+2=$13883.33I=( $15000)(5)+( $15000−$2000)(2)+( $15000−$2000−$1500)(3)+( $15000−$2000− $1500+$4000)(2)5+3+2+2=$13883.33

Thus, average monthly investment balance for the year is  $13883.33.