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Chris invests a total of $19,000 in two accounts. The first account earned a rate of return of 13% (after a year). However, the second account suffered a 2% loss in the same time period. At the end of one year, the total amount of money gained was $1,495.00. How much was invested into each account

Respuesta :

Shahzaibfaraz

Answer:

Amount invested in account with 13% return = $12499.97 rounded off to 12500

Amount invested in account with -2% return = 6500.03 rounded off to 6500

Explanation:

To calculate the amount invested in each account, we must first calculate the total return earned by Chris as a percentage of his investment.

Total Return/gain = 1495 / 19000  = 0.078684 or 7.8684%

To calculate the overall return, we must use the weighted average of returns provided by each account. The weighted average can be calculated as follows,

Average Overall Return =  wA  *  rA  +  wB  *  rB

Where,

  • w represents the weight of investment in each account as a percentage of overall investment
  • r represents the return provided by each account

Let weight of investment in account that provided 13% return be x

Let weight of investment in account that provided -2% return be (1 - x)

0.078684  =  x  *  0.13  +  (1-x)  *  -0.02

0.078684  =  0.13x  -  0.02  +  0.02x

0.078684 +  0.02  =  0.15x  

x = 0.098684 / 0.15

x = 0.65789333333 or 65.789333333%

Amount invested in account with 13% return = 19000 * 65.789333333%

Amount invested in account with 13% return = $12499.97 rounded off to 12500

Amount invested in account with -2% return = 19000 * (1 - 65.789333333%)

Amount invested in account with -2% return = 6500.03 rounded off to 6500

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