I have a problem with a question, I don't know if the question is well worded, it reads as follows
Having the following information about a loan:
Interest rate: 11.5% per annum, compounded monthly.
Payment frequency: monthly
Number of payments: 360
Calculate the Macaulay duration for the loan (in years).
I don't think I can do this because I don't have all the information, but I saw this [https://math.stackexchange.com/questions/502697/compound-interest-confirming-answer]
I hope you can help me and if something is not understood in my question I ask you an apology it is not my mother tongue.
$\require{enclose}$ Assume the monthly payment is $X$. Furthermore, suppose $i^{(12)} = 0.115$, so that the effective monthly rate is $j = i^{(12)}/12 = 0.00958333$, and $n = 360$ months. Payments on the loan are made in arrears. The Macaulay duration (in months) is $$\frac{1}{X a_{\enclose{actuarial}{360}j}} \sum_{t=1}^{360} t X v_j^t = \frac{(Ia)_{\enclose{actuarial}{360}j}}{a_{\enclose{actuarial}{360}j}} = n + \frac{1}{1-v_j} - \frac{n}{1 - v_j^n} \approx 93.3427,$$ where $v_j = 1/(1+j) \approx 0.990508$ is the monthly present value discount factor. The first thing to note is that the $X$ cancels, so the Macaulay duration does not depend on the amount of payment, assuming the payment structure is level.