A loan shark in a student residence lends money on the follo

A loan shark in a student residence lends money on the following terms: \"If I give you $50 on Monday, you owe me $60 on the following Monday. If you are not able to pay back, the amount of money you owe to me will compound.\" (a) What is the nominal interest rate per year the loan shark is charging? (b) What is the effective interest rate per year the loan shark is charging? (c) How mu C h money would you owe to the loan shark if you delay repaying capital and interest to him for one year (52 weeks)?

Solution

Weekly effective rate = {(difference payment) / (Loan taken)} × 100

                                   = ($10 / $50) × 100

                                   = 20%

a.

Nominal interest rate = (Weekly effective rate) × Number of weeks in a year

                                   = 20% × 52

                                    = 1040% per year

b.

Effective interest rate = {1 + (i/n)}^52 – 1

                                    = {1 + (1040%/52)}^52 – 1

                                    = (1.2)^52 – 1

                                    = 13104.63 – 1

                                    = 13103.63 × 100

                                    = 1310363%

c.

Due amount for loan = $50 (1 + 0.2)^52 = $655,231.5