# Loan: calculate number of monthly payments with fixed annual interest, fixed montly payment, and 1 additional payment per year

The situation is the following. Consider a loan of 430,000 units (dollars or whatever).

• The client will pay 10,000 units per month.
• The client will pay an additional 70,000 units every 12th month of the year.
• Annual interest rate is fixed to be 9%.

How do I calculate the number of monthly payments (schedule plan)? How do I calculate the total cost of the credit?

• It's a homework question. Show your work. What have you tried? What tools are you advised to use in your class [will you need to show your work on paper? Will you be tested online with Excel? Will you have a financial calculator?]. Homework questions can be on-topic here, but you won't get responses if you don't show your attempt so someone can see where you are misunderstanding. Commented Dec 1, 2023 at 14:53
• @Grade'Eh'Bacon Funny how "homework question" is assumed here, I am not in this field at all. I posted my question here because I know nothing about these things, and wanted to know the procedure. Commented Dec 1, 2023 at 14:57
• "I posted because I wanted to know the procedure" - why? Why did you pick an esoteric algebra question with [random?] numbers that look picked straight out of a textbook? Homework or not, what is your actual question apart from "how do I insert these numbers into a financial calculator?". Have you tried to solve it yourself? What part is giving you difficulty? How did this question arise? Is someone offering you a financial product and you are trying to double-check it? Commented Dec 1, 2023 at 15:12
• @Grade'Eh'Bacon "Why?" Because I made this loan to someone, but I wanted to leave personal details out and be concise, as is customary in SE sites. If you had checked my profile, you would have seen that I never deal with issues such as this one. As for the "financial calculator", I did not know they existed. This shows how clueless I am about finance, but maybe you can tell me which one I should use instead of turning this whole thing into an inquisition. Commented Dec 2, 2023 at 7:47
• You made a 430k loan without understanding how to calculate interest rates? You invented a new method of assigning an additional annual payment on top of monthly compounded interest for no reason whatsoever? I don't think so. Commented Dec 4, 2023 at 14:14

There may not be a closed-form formula to determine the length due to the extra periodic payment, but the algorithm can be done fairly easily in a spreadsheet:

You need 5 columns: Month, Payment, Interest, Principal, and Balance. Start with the "zero" row with the initial balance in the "Balance" column use the following formulas in each column starting in row 1:

• Payment: payment amount (accounting for the extra payment every 12th month)
• Interest: Previous month's balance * interest_rate / 12
• Principal: Payment - Interest
• Balance: Previous Row's Balance - Principal

Copy the formulas down until you get to a zero or negative Balance (you could adjust the last payment for the final month to get the balance to exactly zero, but since you just want the length and total interest you just need the formulas up to the row that clears the balance)

The total financing cost will be the sum of the interest column.

If you want to check your work, by my calculations it would take 36 months to pay off the loan with a total interest amount of just over 60,000 units.

• This is exactly what I was looking for. Thanks Commented Dec 2, 2023 at 14:21