Question

A bank loaned out ​$13 comma 00013,000​, part of it at the rate of 8 %8% per year and the rest at 18 %18% per year. If the interest received in one year totaled ​$20002000​, how much was loaned at 8 % ?

Answer 1

Answer:

$3400 was loaned out at 8% and $9600 was loaned out at 18%

Step-by-step explanation:

Let Amount loaned out at 8%=$A

Let Amount loaned out at 18%=$B

Total Amount Loaned = $13,000

A + B = 13000 .....(i)

Simple Interest = $\frac{Principal X Rate X Time}{100}$

Interest on A=$\frac{A X 8 X 1}{100}=\frac{8A}{100}$

interest on B=$\frac{ BX 18 X 1}{100}=\frac{18B}{100}$

Total Interest = $\frac{8A}{100}+\frac{18B}{100}=\frac{8A+18B}{100}$

So,$\frac{8A+18B}{100}=2000$ i.e. $8A+18B=200000$......(ii)

Next we solve the two equations simultaneously

A + B = 13000 .....(i)

$8A+18B=200000$ ......(ii)

From (i) A=13000-B

Substituting into (ii)

8(13000-B)+18B=200000

104000-8B+18B=200000

10B=200000-104000=96000

B=9600

Recall A + B = 13000

A + 9600 = 13000

A=13000-9600=3400

Therefore: A= $3400 and B=$9600