Loan Shark rates of interest

[tseki]

Hi,

I am having a problem calculating the annual interest to this question.

If I borrow $1000 from a loan shark and pay him back in 10 weekly payment of $150, what is the effective annual rate of interest? I thought it was 1.5 to the power of 5.2, which is the number of periods of 10 weeks in a year. I think it is simple but I don't know how to do it.

Regards,

T

 

[mmm4444bot]

Are loan sharks savvy enough to compound interest?

From Wikipedia: A nominal rate without the compounding frequency is not fully defined: for any interest rate, the effective interest rate cannot be specified without knowing the compounding frequency and the rate.

So, let's look at simple interest, instead.

(If you have knowledge that the interest is compounded, you can let us know the compounding period.)

With simple interest: 0.5 * 5.2 = 2.6

The effective rate for one year is 260% percent (hmmm, so much better than Money Tree).

Here's another way to reason it out.

Clearly, the interest rate for the 10-week loan period is 50%, right?

The formula for simple interest follows.

I = P * r * t

where I is the interest earned, P is the principal, r is the decimal form of the annual interest rate, and t is the number of years invested.

The interest earned is $500, and the principal is $1,000, so I = 500 and P = 1000.

A 10-week period represents 10/52nds of a year. That ratio reduces to t = 5/26.

500 = 1000 * r * 5/26

Solving for r, we get: (26/5)(500/1000).

r = 2.6

Cheers ~ Mark