A sum of money is due in 2 months. What Will be the discount rate,which is equivalent to 18% interest rate
To determine the discount rate that is equivalent to an 18% interest rate over 2 months, we can use the formula for calculating compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan (or the amount due)
P = the principal amount (or the initial loan amount)
r = the annual interest rate
n = the number of times that interest is compounded per year
t = the time in years
In this case, we want to find the discount rate (r) that is equivalent to 18% interest over 2 months. Since there are 12 months in a year, we divide the time (t) by 12 to convert months to years.
Let's say the amount due is $1,000.
Using the formula, we can rearrange it to solve for r:
r = (A/P)^(1/(nt)) - 1
Substituting the given values:
A = $1,000
P = $1,000
r = discount rate (to be determined)
n = 1 (assuming the interest is compounded annually)
t = 2/12 (2 months divided by 12 to convert to years)
r = ($1,000 / $1,000)^(1 / (1 * 2/12)) - 1
r = (1)^(1 / (1/6)) - 1
r = 1^6 - 1
r = 1 - 1
r = 0
So the discount rate that is equivalent to an 18% interest rate over 2 months is 0%.