Nominal and effective interest rates

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• 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?

Here are my answers:

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)