Question

Mr tally inherited $200,000 he used a portion of the inheritance to build a house he invested the rest of the money for 1 year as follows. 1/3 at 12 % two thirds at 15% the interest from both investments was $8,400 how much did it cost to build the house?

Answer 1

The general formula to solve this problem is the following:

`200,000=H+I`

Where, 200,000 is the money inherited, H is the cost of building the house and I is the money invested.

In order to find the amount of money invested, we need to use, the simple interest formula. The simple interest formula is the following:

`A=I\cdot r\cdot t`

where,

A is the amount earn, $8400 in this case

I is the amount invested,

r is the interest rate and

t is time, 1 year in this case

For this example, since the investment was divided in two parts, there are two values for r, therefore the formula to find 'I' will be the following:

`A=(1)/(3)\cdot I\cdot0.12+(2)/(3)\cdot I\cdot0.15=8400`

now, let's solve for I . I will show you the steps

`((0.12)/(3)+(2\cdot0.15)/(3))\cdot I=8400`
`0.14\cdot I=8400`
`I=(8400)/(0.14)=60000`

Therefore, the value invested was 60,000

If I = 60,000, then the value to build the house is $140,000

`\begin{gathered} 200,000=H+60,000 \\ H=200,000-60,000 \\ H=140,000 \end{gathered}`