Hi, thanks for the reply. They didn't give me a formula. The only information I got from them was that "Interest is charged at the rate of 5/6 of 1% per month until paid (interest is calculated daily)"
I believe the compounding period is a month, because they say that the interest is "5/6 of 1% per month". So [imath]t[/imath] should stand for the number of months.
I would assume that, for ease of calculations, they want you to assume that every month has thirty days. So, because they are compounding daily, there will be thirty compoundings per one-month period.
The formula I've been trying is what I came up with but I don't think it's right:
Future Value = Present Value * (1 + Interest Rate / Compounding Frequency) ^ (Number of Years * Compounding Frequency)
Future Value = 172.14 * (1 + 10% / 365 ) ^ (0.419178082 * 365 )
Where number of years in this specific example would be 153 days/365 days = 0.419178082 years
5/6 of 1% per month * 12 months = 10% per year
The compound-interest formula is:
[imath]\qquad A = P\left(1 + \frac{r}{n}\right)^{nt}[/imath]
...where [imath]A[/imath] is the ending amount, [imath]P[/imath] is the beginning amount (or "principal"), [imath]r[/imath] is the interest rate (expressed as a decimal), [imath]n[/imath] is the number of compoundings per period, and [imath]t[/imath] is the number of periods.
The future-value formula is:
[imath]\qquad FV = PV\left(1 + \frac{r}{n}\right)^{nt}[/imath]
...where [imath]FV[/imath] is the future value and [imath]PV[/imath] is the present value. Yes, they're the same, other than for the names on two of the variables.
I would do the computations with [imath]PV = 172.14[/imath], [imath]r = \left(\frac{5}{6}\right)\left(\frac{1}{100}\right) = \frac{1}{120}[/imath] (use the exact value), [imath]n = 30[/imath], and [imath]t = \frac{153}{30}[/imath] (again, use the exact value).