In the **Simple Interest Problems Series**, we have learned how to calculate the interest, rate, or time of the principal invested. In that series, the principal is invested to a single bank or company. In this series, we will learn how to calculate the interest of money invested at different companies (different rates). Before starting with our first example, familiarize yourself with the following terms:

principal – the amount of money invested

rate of interest – the percent of interest yearly or any period of time (e.g. monthly, quarterly)

interest – income or return of investment

Hence, if Php10000 is invested at a bank with 3% interest is 300, Php10000 is the principal, 3% is the rate of interest, and 300 is the interest.

**Example 1**

Mr. Molina invested Php100,000.00. A part of it was invested in a bank at 4% yearly interest and another part of it at a credit cooperative at 7% yearly interest. How much investment he made in each if his yearly income from the two investments is Php5950.00?

*Scratch Work*

If we let x be the money invested at a bank, then 100000 – x is the amount invested at the credit cooperative. To calculate for the interest, we must apply the percent of each interest at each amount. That is

(4%)(x) = yearly interest from at the bank

(7%)(100000 – x) = yearly interest from the credit cooperative

If we add the interest, it will amount to Php5950. So, here’s our solution.

*Solution*

Let x = amount of money invested at the bank

100000 – x = amount of money invested at the credit cooperative

Total Interest = Interest From the Bank + Interest from the Credit Cooperative

5950 = (4%)(x) + (7%)(100000 – x)

We need to convert percent to decimals in order to multiply. We do this by dividing the percentage by 100. So, 4% = 0.04 and 7% = 0.07. Substituting to the previous equation, we have

5950 = (0.04)(x) + (0.07)(100000 – x)

5950 = 0.04x + 7000 – 0.07x

5950 – 7000 = -0.03x

-1050 = -0.03x.

We can eliminate the decimals by multiplying by 100.

-105000 = -3x

Dividing both sides by -3, we have

35000 = x.

That means that Mr. Molina invested Php35000 in the bank and Php100000 – Php35000 = Php65000 in the credit cooperative.

Check

(4%)(35000) + (7%)(65000) = (.04)(35000) + (.07)(65000)

= 1400 + 4550 = 5950

As we can see, our interest from the two investments is Php5950.00

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