Question

Chris's bank offers him 2 types of investment, one at 4% and the other at 7% He invested $1500 more at 7% than at 4%. How much was invested at each rate if the total interest after a year was $460

Answer 1

Chris invested $3227.27 at a 4% interest rate and $4727.27 at a 7% interest rate to achieve a total interest of $460 after one year.

Step-by-step explanation:

Chris wants to invest his money in two different accounts. He chooses to invest $1500 more in the account yielding 7% than the one yielding 4%. If the total interest from both accounts is $460 after one year, we need to figure out how much was invested into each account.

We can set up a system of equations to represent this situation:

1. Let x be the amount invested at 4%.
2. Then x + $1500 is the amount invested at 7%.
3. The total interest from both accounts is the sum of the individual interests: 0.04x + 0.07(x + $1500) = $460.

Solving this system, we perform the following steps:

1. Multiply the terms inside the brackets: 0.04x + 0.07x + $105 = $460.
2. Combine like terms: 0.11x + $105 = $460.
3. Subtract $105 from both sides: 0.11x = $355.
4. Divide by 0.11: x = $3227.27.
5. Add $1500 to find the amount at 7%: $3227.27 + $1500 = $4727.27.

Therefore, Chris invested $3227.27 at 4% and $4727.27 at 7%.