# Nominal and effective interest rates

• Mar 4th 2010, 04:23 AM
enchanteuse
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.
• Mar 4th 2010, 12:23 PM
Wilmer
enchanteuse? same as "femme fatale"? (Giggle)

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 (Nerd)