# A man invested some amount at 6% interest rate and some amount at 9% interest rate. If he put Php12,000 more in the second investment than in the first investment and his annual income from both investments is Php4,830 how much did he invest at each rate?

Jun 19, 2016

The principle sums were Php25000 and Php37000

#### Explanation:

$\textcolor{b r o w n}{\text{Type of interest not given}}$

Let the first principle sum be ${P}_{1}$
Let the second principle sum be ${P}_{2}$

Then we have:

As the annual income is fixed then the interest rate can not be compound. Otherwise the income each year would increase.

${P}_{1} \left(\frac{6}{100}\right) + {P}_{2} \left(\frac{9}{100}\right) = \frac{4830}{\text{year}}$

But ${P}_{2} = {P}_{1} + 12000$

So by substitution we have:

${P}_{1} \left(\frac{6}{100}\right) + \left({P}_{1} + 12000\right) \left(\frac{9}{100}\right) = \frac{4830}{\text{year}}$

$\frac{1}{100} \left(6 {P}_{1} + 9 {P}_{1} + 108000\right) = 4830$

$15 {P}_{1} = 483000 - 108000$

$\textcolor{b l u e}{{P}_{1} = 25000}$

$\textcolor{b l u e}{\implies {P}_{2} = {P}_{1} + 1200 \to 25000 + 12000 = 37000}$