Question

HELP ME PLEASE. Anson borrows some money from a bank at a rate of 10% simple interest for 1 year. Jenny borrows $1000 more then Anson from another bank at 8% simple interest for 6 months
If the total interest paid by Anson and Jenny is $740, What is the amount of money Anson borrowed?

A 1250

B 3750

C 4070

D 5000
Please show your work

Answer 1

$5000 is the correct answer.

The formula for simple interest is I=prt.  Anson gets 10% interest; 10% = 10/100 = 0.1.  This gives us
I=p(0.1)(1) = 0.1p.

Jenny borrows 1000 more than Anson, so her principal is p+1000.  Her rate is 8%; 8%=8/100 = 0.08.  She invests it for half of a year, or 0.5. Together this gives us:
I=(p+1000)(0.08)(0.5)
= (p+1000)(0.04)
= p*0.04 + 1000*0.04
= 0.04p + 40

Together they earned 740:
0.1p+0.04p+40 = 740

Combine like terms:
0.14p+40 = 740

Subtract 40 from both sides:
0.14p+40-40 = 740-40
0.14p = 700

Divide both sides by 0.14:
0.14p/0.14 = 700/0.14
p = 5000