Word Problem

Question

Laura borrowed a total of $20,000 from two different banks to start a business. One bank charged the equivalent of 6% simple interest, and the other charged 7.5% interest. If the total interest after 2 years was $2460, determine the amount borrowed from each bank.

Answer 1

X is the amount borrowed at 6% = 0.06

Y is the amount borrowed at 7.5% = 0.075

the SIMPLE interest after 2 years for each loan is:

2*0.06x = 1.2x and 2*0.075y 0.15y

0.12x + 0.15y = 2460

BUT...

x + y = 20000

y = 20000 - x

0.12x + 0.15(20000 - x) = 2460

0.12x + 3000 - 0.15x = 2460

-0.03x + 3000 = 2460

-0.03x = -540

3x = 54000

x = 18000

which forces y = 2000

check:

the simple interest after 2 years is:

2 * 0.06 * 18000 + 2* 0.075*2000 =

2160 + 300

2460

18000 borrowed at 6% and 2000 borrowed at 7.5%