Question

A bank loaned out $20,000, part of it at the rate of 8% per year and the rest at 13% per year. If the interest received in one year totaled $2000, how much was loaned at 8%?

Answer 1

The formula for calculating simple interest is expressed as

I = PRT/100

where

I is interest

P = principal or amount loaned

r = interest rate

t = number of years

Let x represent the amount loaned at 8%

Let y represent the amount loaned at 13%

Since the total sum was 20000, it means that

x + y = 20000

x = 20000 - y

For the loan at 8%,

P = x

R = 8

T = 1 year

I = x * 8 * 1/100 = 0.08x

For the loan at 13%,

P = y

R = 13

T = 1 year

I = y * 13 * 1/100 = 0.13y

Since the interest received is 2000, it means that

0.08x + 0.13y = 2000

Substituting x = 20000 - y into 0.08x + 0.13y = 2000, we have

0.08( 20000 - y) + 0.13y = 2000

1600 - 0.08y + 0.13y = 2000

- 0.08y + 0.13y = 2000 - 1600

0.05y = 400

y = 400/0.05

y = 8000

x = 20000 - y = 20000 - 8000

x = 12000

The amount loaned at 8% is $12000 and the amount loaned at 13% is $8000