Answer:
The loaned amount at 11 % is $ 19,000
The loaned amount at 10 % is $ 2,500
Step-by-step explanation:
Given as :
The total loan amount = $21,500
The total interest earn = $2,340.00
The rate of interest are 11 % and 10 %
Let The loan amount at 11 % rate = $P
and The loan amount at 10 % rate = $21,500 - $P
Let The loan took for 1 year
Now,<u> From Simple Interest method </u>
Simple Interest = ![\dfrac{\textrm Principal\times \textrm Rate\times \textrm Time}{100}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20Principal%5Ctimes%20%5Ctextrm%20Rate%5Ctimes%20%5Ctextrm%20Time%7D%7B100%7D)
= ![\dfrac{P_1\times R_1\times \textrm Time}{100}](https://tex.z-dn.net/?f=%5Cdfrac%7BP_1%5Ctimes%20R_1%5Ctimes%20%5Ctextrm%20Time%7D%7B100%7D)
Or,
= ![\dfrac{P\times 11\times \textrm 1}{100}](https://tex.z-dn.net/?f=%5Cdfrac%7BP%5Ctimes%2011%5Ctimes%20%5Ctextrm%201%7D%7B100%7D)
Similarly
= ![\dfrac{21,500 - P\times 10\times \textrm 1}{100}](https://tex.z-dn.net/?f=%5Cdfrac%7B21%2C500%20-%20P%5Ctimes%2010%5Ctimes%20%5Ctextrm%201%7D%7B100%7D)
∵
+
= $2,340
Or,
+
= $2,340
Or, 11 P - 10 P + 215000 = 234000
Or, P = 234000 - 215000
∴ P = $ 19,000
And $21,500 - $ 19,000 = $ 2,500
Hence The loaned amount at 11 % is $ 19,000
And The loaned amount at 10 % is $ 2,500 Answer