Question

David used part of $100,000 to purchase a house. Of the remaining portion, he invested 1 3 of it at 4 percent simple annual interest and 2 3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320, what was the purchase price of the house?

Answer 1

The purchase price of the house is $94,000

Step-by-step explanation:

Let the amount invested by David be b, then the amount used to purchase the house would be 100,000 - b

If he invested 1/3 of it at 4 percent simple annual interest and 2/3 of it at 6 percent simple annual interest. If after a year the income from the two investments totaled $320

Then,

`(1)/(3)b × 4% + (2)/(3)b × 6% = 320`

`(b)/(3) × (4)/(100) + (2b)/(3) × (6)/(100)  = 320`

`(4b)/(300) + (12b)/(300) = 320`

`(16b)/(300) = 320`

16b = 320 × 300

b = 320 × 300/16

b = 6,000

Therefore, the cost of the house (100,000 - b)

= 100,000 - 6,000

= $94,000