|
Question 1141252: A $900 credit card debt was to be repaid in 12 months. If $14500 was repaid, what was the nominal rate compounded daily that was charged?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.
in your problem, the formula becomes 14500 = 900 * (1 + r) ^ 365.
f = 14500
p = 900
n = 1 year * 365 days per year = 365 days.
divide both sides of the equation by 900 to get 14500 / 900 = (1 + r) ^ 365.
take the 365th root of both side of the equation to get (14500 / 900) ^ (1 / 365) = 1 + r.
subtract 1 from both sides of the equaiton to get (14500 / 900) ^ (1 / 365) - 1 = r
solve for r to get r = .0076441622 per day.
multiply that by 365 to get 2.790119191 per year * 100 = 279.011919% per year.
that's the nominal interest rate percent per year.
the effective interest rate per year would be (1 + .0076441622) ^ 365 - 1 = 16.11111111 * 100 = 1611.1111111% per year.
confirm by replacing r in the orginal equation with .076441622 to get 14500 = 900 * (1 + .0076441622) ^ 365 to get 14500 = 14500 which confirms that the solution is correct.
when the time period is in days, the interest rate per year is divided by 365 to get the interest rate per day and the number of years is multiplied by 365 to get the number of days.
that's the generally accepted convention as far as i know.
|
|
|
| |
