A bank loaned out $67,000, part of it at the rate of 14% per year and the rest at a rate of 6% per year. If the interest received was $6100, how much was loaned at 14%?

1 Answer
Nityananda
May 18, 2017

$26,000

Explanation:

Let the person loaned at 14% is $x. So loaned at 6% is $(67,000 - x).

We know, #color(red)[Interest = (pnr)/100]#

#color(green)(For the 14% case)# : Principal (P) = $x, Year(n) = 1 and Rate of Interest (r) = 14%. Interest = pnr/100 = [ x114]/100 = 14x/100.

#color(red)( for the 6% case)# : Principal(p) = $(67,000 - x), year(n) = 1 and Rate of Interest(r) = 6. So Interest = [pnr]/100 = [(67,000 - x)16]/100.

Now as per question,
Total Interest = two parts of interest.
Hence, 14x/100 + [6(67,000 - x)]/100 = $6100

#rArr (14x)/100 + 402000/100 - (6x)/100 = 6100#

#rArr (8x)/100 = 6100 - 4020 = 2080#

#rArr x = 2080*100/8 = 26,000 #

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