Question

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

Answer 1

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

Step-by-step 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