Question

Helen Weller invested $10,000 in an account that pays 12% simple interest. How much additional money must be invested in an account that pays 15% simple interest so that the total interest is equal to the interest on the two investments at the rate of 13%?

Answer 1

Let's denote:

- the amount of money Helen Weller needs to invest in the account that pays 15% interest as x,

- the total amount of money in both accounts as y = $10,000 + x.

According to the problem, the total interest from the two investments should be equal to the interest from a single investment at a 13% rate. This translates to the following equation:

(12% * $10,000) + (15% * x) = 13% * y.

Substituting y = $10,000 + x into the equation gives us:

(12% * $10,000) + (15% * x) = 13% * ($10,000 + x).

Now we can solve this equation to find the value of x.

Let's convert all percentages to decimals (12% = 0.12, 15% = 0.15, 13% = 0.13) and solve for x:

0.12 * $10,000 + 0.15x = 0.13 * ($10,000 + x),

$1,200 + 0.15x = $1,300 + 0.13x,

0.02x = $100,

x = $100 / 0.02,

x = $5,000.

Therefore, Helen Weller needs to invest an additional $5,000 in the account that pays 15% interest to ensure the total interest from both investments is equal to a single investment at a 13% rate.