Question

A bank loaned out $21,500 , part of it at the rate of 11% annual interest, and the rest at 10% annual interest. The total interest earned for both loans was $2,340.00 . How much was loaned at each rate?
____ was loaned at 11%
____ was loaned at 10%

Answer 1

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, From Simple Interest method

Simple Interest = $\dfrac{\textrm Principal\times \textrm Rate\times \textrm Time}{100}$

$SI_1$ = $\dfrac{P_1\times R_1\times \textrm Time}{100}$

Or, $SI_1$ = $\dfrac{P\times 11\times \textrm 1}{100}$

Similarly

$SI_2$ = $\dfrac{21,500 - P\times 10\times \textrm 1}{100}$

∵  $SI_1$ +  $SI_2$ =  $2,340

Or, $\dfrac{P\times 11\times \textrm 1}{100}$ + $\dfrac{21,500 - P\times 10\times \textrm 1}{100}$ = $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