# Thread: Nominal and effective interest rates

1. ## Nominal and effective interest rates

Problem statement: A loan shark lends someone money saying, "If I lend you $50 on Friday, you owe me the$50 plus an extra $10 on the following Friday." (The lending goes on for a year) a) What is the nominal interest rate per year being charged? b) What effective interest rate is the loan shark charging? c) If the loan shark started with$50, and was able to keep it, and all the money received loaned out at all times, how much does he have at the end of one year?

a) (10/50)*(365/7) = 10.42 = 1042%

b) i = e^x-1
i = e^10.42-1 = 33 522.43 = 3 352 243.42%

c) I'm not sure how to do c

My numbers are very large. Is that normal? Please correct me if I'm wrong because these numbers are just outrageous.

2. enchanteuse? same as "femme fatale"?

a) Well, $10 on$50 for a week is obviously 20% per week.
As simple annual interest: 52 * 20 = 1040%

b) effective = 1.2^52 - 1 = 13104.63... - 1 = 13103.63...%
YES: means $1 accumilates to ~$13,104 over 1 year!

c) if that means he reinvests the interest at same rate, like a week
after the initial $50, he lends$60 and collects $72 ($12 interest):
Code:
week             interest        worth
0                  0             50
1                 10             60
2                 12             72
.....
51              91004         546026
52             109206         655232
YES: that's 655,232 bucks