Ann's $9,300 savings is in two accounts. One account earns 4% annual interest and the other earns 9%. Her total interest for the year is $697. How much does she have in each account?

Question

Ann's $9,300 savings is in two accounts. One account earns 4% annual interest and the other earns 9%. Her total interest for the year is $697. How much does she have in each account?

Answer 1

There are two unknown values to solve for: the amount in the first account, x, and the amount in the second account, y. Because of this, we expect to have two equations to have enough information to solve for x and y. Well, we know that 9300 = x + y (that's what Ann has now) and that the interest that will be gained this year through both accounts is $697. We know that the interest gained in an interval of time is the amount at the end of the interval minus the amount at the beginning. Since we have the interest and the starting amount, we can find the amount after the year is up by doing $9300 + $697 = $9997. We also know that after a year elapses, the total amount of money in each account due to interest will be x(1+0.04) + y(1+0.09). We know then that 9997 = ???. Can you take it from here?