Question

d. In the poor areas of many cities around the world, we find people offering pay-day loans. One loan agency in Dacca offers to loan Gita $20 till her pay cheque arrives in two weeks time. When it arrives, she must pay back the $20 plus a $3 service charge. What is the effective annual interest rate she is paying on the loan? (3 pts) You can make monthly deposits into a savings account that pays interest at a nominal rate of 18% per year, compounded monthly. five years time? (3 pts) e. How much should you deposit each month if you want to have $7,000 in

Answer 1

(d)

Interest rate charged for 2 weeks = ($3 / $20) x 100% = 15%

Annual Effective interest rate (EAR) = [1 + r]^N - 1, where N: Number of compounding periods

r = 15% = 0.15, N = 52 weeks / 2 weeks = 26

EAR = [1 + (0.15]²⁶ - 1 = (1.15)²⁶ - 1 = 37.8568 - 1 = 36.8568 = 3,685.68%

(e)

Monthly nominal interest rate = 18%/12 = 1.5%

Number of months = 5 x 12 = 60

Monthly deposit ($) = Future value / F/A(1.5%, 60) = 7,000 / 96.2147** = 72.75

**F/A(1.5%, 60) = [(1.015)⁶⁰ - 1] / 0.015 = (2.4432 - 1) / 0.015 = 1.4432 / 0.015 = 96.2147