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

The loaned amount at 11 % is $ 19,000

The loaned amount at 10 % is $ 2,500

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 =
`(\textrm Principal* \textrm Rate* \textrm Time)/(100)`

`SI_1` =
`(P_1* R_1* \textrm Time)/(100)`

Or,
`SI_1` =
`(P* 11* \textrm 1)/(100)`

Similarly

`SI_2` =
`(21,500 - P* 10* \textrm 1)/(100)`

∵
`SI_1` +
`SI_2` = $2,340

Or,
`(P* 11* \textrm 1)/(100)` +
`(21,500 - P* 10* \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