What interest rate would you be paying if you borrowed $1,000 for 6 months and paid $60 in interest?

Question

What interest rate would you be paying if you borrowed $1,000 for 6 months and paid $60 in interest?

Answer 1

$1,000 for 6 months, yields $60 interest

A = P(1+r/n)^nt

A = ending Amount = 1060

P= starting deposit = 1000

r = annual interest rate

n = compounding periods per year = 1

t = number of years = half a year = 6 months

1060 = 1000(1+ r)^.5

1060/1000= 106/100

= 1.06 = (1+r)^(1/2)

square both sides

1.06^2 = 1+r

1+r = 1.06

r = 1.123600-1

r = .123599

r= about 12.36%

in one year

60 is 6% of 1000

.06 x 1000 = 60

in half a year

60 is about 12% of 1000

.(.12 x 1000)/2 = 120/2 =60

or try continous compounding, a lower limit on r

1060 = 1000e^.5r

106/100 = e^.5r

ln1.06 = .5r

r = 2ln1.06

r = about 11.65%

just call it 12% APR, regardless of any compounding or not

or

it's 6% semi-annual interest rate

or

if you're the quick pay day loan shark company and want to make it sound like a real bargain

call it 2% monthly interest

or even call it the smallest interest rate ever: 0.07% daily interest rate