Interest is charged at the rate of 5/6 of 1% per month until paid (interest is calculated daily)

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mtmtnman

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Hi, how would you set this formula up to find the future value of $172.14, 153 days later?

Interest is charged at the rate of 5/6 of 1% per month until paid (interest is calculated daily)
 
mtmtnman said:
Hi, how would you set this formula up to find the future value of $172.14, 153 days later?

Interest is charged at the rate of 5/6 of 1% per month until paid (interest is calculated daily)
Click to expand...

What formula did they give you for finding the future value (FV) of an investment? How far have you gotten in applying this information?

Please be complete. Thank you!
 
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)"

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
 
mtmtnman said:
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)"
Click to expand...

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.

mtmtnman said:
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
Click to expand...

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).
 
stapel said:
I believe the compounding period is a month, because they say that the interest is "5/6 of 1% per month". So ttt should stand for the number of months.
Click to expand...
Not sure I agree. In a typical US mortgage the interest is compounded/computed monthly but the annual rate is usually specified. Could this be interpreted as a daily interest of (5/6) / 30.4375, where 30.4375 is a number of days in an average month (=365.25 / 12) ? But in the end this is for the OP to clarify.
 
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