Word Problems - solve a system of equations for each problem

Question

Georgina has a total of $5000 invested in a savings account that receives 0.6% APY and a CD that receives 0.9% APY. How much does she have invested in each account if her total annual interest earned is $37.50?

Answer 1

I have a long digression/background below, but first let's just solve the equation as stated, which has one unknown variable (amount in CD).

5000*0.6% + CD*0.9% = 37.50

rearrrange to get CD on its own...

CD = (37.50 - 5000*0.06%)/0.9% = 833.3333333 (recurring decimal which as you know is 1/3)

I'd therefore round down to the nearest dollar and say Georgina's CD has $833. A CD like this is rather unlikely, and would not typically be used in these types of problems (rather nice round numbers like $50, $100, $5000) so in an exam such an answer would make me think I was wrong. However, I think in this case, Mark U. has simply asked a non-exam question.

Checking my working (always a good idea, if you have time): The interest on $5000 (in savings) at 0.6% is $30. The interest on $833 (in CD) at 0.9% = $7.497 which would be rounded to $7.50. The total is $37.50, as stated in the question.

If you want more discussion, here's my digression:

Firstly, 0.6% and 0.9% are very low rates of interest, certainly less than the rate of inflation. Which means that your savings are LOSING value each year. Hence, while CDs/savings accounts are very safe (FDIC protected), it's much more effective to invest any spare funds in paying down high interest debt (credit cards, etc.) first. If you're fortunate to be debt-free, then consider investing in the stock market (higher returns, historically), or yourself (upgrading your education for better paying career, starting your own business, etc.).

Secondly, Mark U. has used APY, a financial term.

For interest, we can say that the Principal Amount * interest rate = interest paid.

APY stands for Annual Percentage Yield. It is actually is a measure of "compound" interest rather than "simple" interest. Simple interest is calculated only on the principal, while compound interest is calculated on the principal plus any interest already added. As the problem does not mention compounding, or the frequency of interest payments, then I think we're safe to assume that it's an annual interest payment, which means that, in this case, APY is the same as simple interest.

Putting this in numbers, we can say that APY = (1 + period interest) raised to the power of number of periods - 1

For one period (ie annual interest payment) the power is 1 and doesn't change anything.

APY = (1+0.06) - 1 = 0.06

Again, in an exam, it's more likely that the question explicitly states simple or compound interest rather than using APY. Moreover, if the question refers to compound interest, then it will also include the period (monthly, quarterly, annually).