Jacob deposited a total of $2000 with two different savings institutions.

Question

Jacob deposited a total of $2000 with two different savings institutions. One pays interest at a rate of 4% per year, whereas the other pays interest at a rate of 10% per year. If Jacob earned a total of $140 in interest during a single year, how much did he deposit in each institution?

a) List and verbally define your variables.

b) Set-up the appropriate system of equations.

c) Solve the problem:

Answer 1

Here's what we are going to do:

a)

Because we have 2,000 to deposit, we can use variables to define the amount that will go into each account.

If we put $x into account 1, then the rest (2,000 - x), will go into account 2.

Account 1 = x

Account 2 = 2,000 - x

b)

Because we are looking to earn interest of $140, we will set our equation equal to that. The amount of interest generated by each account, because the investment is one year, and our rate is annual, will simply be the rate of the account times the amount of money in the account.

Account 1 = 4%

Account 2 = 10%

Therefore our equation is:

0.04*(x) + 0.10*(2,000-x) = 140

c)

0.04x + 200 - 0.10x = 140

-0.06x = -60

x = 1,000

Account 1 = 1,000

Account 2 = 2,000 - 1,000 = 1,000