Question

How many weeks would it take to increase the debt of a simple discount loan by 135% if the annual simple discount rate is 27%? Round your answer to the nearest week.

Answer 1

Let's suppose the initial amount of debt is $100

Now it is to be increased by 135% i.e. by $135

The amount of loan after increase shall be $235 ($100 + $135)

A = P * ( 1 + rt )

where A = amount after the increase

P = initial amount

r = rate per annum

t = no. of years

$235 = $100 * (1 + (27% * t))

1 + (27% * t) = $235 / $100

1 + (27% * t) = 2.35

27% * t = 2.35 - 1

27% * t = 1.35

t = 1.35 / 27%

t (no of years) = 5 years

time in weeks = 5 * 52

time in weeks = 260 weeks

Therefore, it would take 260 weeks to increase the debt of a simple discount loan by 135% is the annual simple discount rate is 27%