Question

A loan shark lends you $50 at 3% compound interest per week (this is a weekly, not an annual rate.) Round your answers to the nearest dollars

A. How much will you owe after 2 years?
B. in "street" language, the profit on such a loan is known as the "vigorish" or the "vig." Find the sharks vig.

Answer 1

(a) Amount owed after 2 years is $ 1081.54

(b) The shark's vig is $ 1031.54

Explanation:

(a)

The amount on a principal, P, after a period, T, at a compound interest, R, is given by

`A = P\left(1+(R)/(100)\right)^T`

From the question,

P = $ 50

R = 3% per week

T = number of weeks in 2 years = 2 × 52 = 104 (Assuming 52 weeks for each year)

`A = \$\,50\left(1+(3)/(100)\right)^(104) = \$\,50(1.03)^(104) = \$\,1081.54`

(b)

The shark's vig = $ 1081.54 - $ 50 = $ 1031.54