|
Question 813657: A bank loaned $68,000, part of it at a rate of 15% per year and the rest at a rate of 5% per year. If the interest received was $6600, how much was loaned at 15%?
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! Let a = the part of the investment earning 15% interest
Let b = the part of the investment earning 5% interest
The total investment is $68,000, so we have
(1) a + b = 68000
The total interest earned, assuming in one year, is
(2) 15% of a + 5% of b = 6600 or
(3) 0.15*a + 0.05*b = 6600
Let's get rid of the decimals in (3) by multiplying both sides by 100 to get
(4) 15*a + 5*b = 660000
Now solve (1) for a to get
(5) a = 68000 - b and put a into (4) to get
(6) 15*(68000 - b) + 5*b = 660000 or
(7) 15*68000 - 15*b + 5*b = 660000 or
(8) 1020000 - 10*b = 660000 or
(9) 10*b = 1020000 - 660000 or
(10) 10*b = 360000 or
(11) b = 36000
Then from (5) we get
(12) a = 68000 - 36000 or
(13) a = 32000
Let's check the answer with (3).
Is (0.15*32000 + 0.05*36000 = 6600)?
Is (4800 + 1800 = 6600)?
Is (6600 = 6600)? Yes
Answer: $32,000 was invested (not loaned) at 15%.
PS Step (4) is not necessary, I just don't like to work with decimals.
PPS The problem statement isn't really correct. You don't receive interest on a loan, so my answer states that it is an investment.
|
|
|
| |
