Question

A payday loan company charges 5.2 percent interest for a two-week period. What would be the annual interest rate from that company?

An ATM with a service fee of $2 is used by a person 200 times in a year. What would be the future value in 10 years (use a 3 percent rate) of the annual amount paid in ATM fees?

Answer 1

Answer 1
Annual Interest rate from the Company = Interest rate for 2 weeks period x [Number of weeks in a year/2]
Annual Interest rate from the Company = 5.2% x [ 52 /2 ] = 135.20%
Answer 2
Annual amount paid in ATM fees = service fee per use x Number of times ATM is used in a year = $2 x 200 times = $400
We can use the future value of annuity to calculate the future value in 10 years of annual amount paid in ATM fees
Future value of annuity = P x {[(1+r)^n -1]/r}
Future value of annuity = Future value in 10 years of annual amount paid in ATM fees = ?
P = annual ATM fees = $400
r = interest rate = 3%
n = number of years = 10
Future value of annuity = 400 x {[(1+0.03)^10 -1]/0.03}
Future value of annuity = 400 x 11.46388
Future value of annuity = 4585.55
Future value in 10 years of annual amount paid in ATM fees = $4585.55