Question

Account a and b each start with $400. If account a earn $45 each year and account b earns 5% of its value each year when will account b have more money than account a

Answer 1

To find when Account B will have more money than Account A, set their balances equal to each other, solve for x, and plug that value back into the equation.

Step-by-step explanation:

To determine when Account B will have more money than Account A, we need to find the number of years it will take for Account B to exceed $400. Each year, Account A earns $45, so after n years, Account A would have a balance of: 400 + 45n.

Account B earns 5% of its value each year. Let's call the number of years it takes for Account B to exceed $400 as 'x'. After x years, Account B's balance would be: 400 * (1 + 0.05)^x. We need to find the value of x where Account B's balance is greater than Account A.

Setting the two equations equal to each other and solving for x:

400 + 45n = 400 * (1 + 0.05)^x

Now we solve for x:

1 + 0.05)^x = (400 + 45n) / 400

x = log((400 + 45n) / 400) / log(1.05)

Using this equation, you can easily calculate the value of x and find out when Account B will have more money than Account A.