On two investments totaling 14,000 Peter lost 4% on one earned 6% on the other if his net annual receipts were 312 how much was each investment
Let's assume the amount invested at 4% is x.
Therefore, the amount invested at 6% is 14000 - x since the total investment is equal to $14000.
Peter lost 4% on one of the investments, so the loss from this investment is 0.04x.
Peter earned 6% on the other investment, so the profit from this investment is 0.06(14000 - x) = 840 - 0.06x.
The net annual receipts are the difference between the profit and loss, which is given as $312.
Therefore, we can write the equation as:
0.06(14000 - x) - 0.04x = 312
Simplifying the equation, we have:
840 - 0.06x - 0.04x = 312
840 - 0.1x = 312
-0.1x = 312 - 840
-0.1x = -528
x = -528 / -0.1
x = 5280
So, Peter invested $5280 at 4% and $14000 - $5280 = $8720 at 6%.