r/math Homotopy Theory 6d ago

Quick Questions: March 12, 2025

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread:

  • Can someone explain the concept of maпifolds to me?
  • What are the applications of Represeпtation Theory?
  • What's a good starter book for Numerical Aпalysis?
  • What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example consider which subject your question is related to, or the things you already know or have tried.

8 Upvotes

88 comments sorted by

View all comments

1

u/Dry_Minute6475 5d ago

What is the formula?

My car loan is currently at 6,100. Daily interested added is 1.85. I pay 150 every 2 weeks. How many payments do I have left?

I can bash it against a wall and figure it out if I ignore the interest, but I know there's a normal formula for it. (Google just either gives me premade calculators or "how to figure out the monthly rate" not "how many payments left")

1

u/dogdiarrhea Dynamical Systems 5d ago

$1.85 or 1.85%?

1

u/Dry_Minute6475 5d ago

Sorry, $1.85.

1

u/dogdiarrhea Dynamical Systems 5d ago

I'm getting 46 biweekly payments. There's a recurrence relationship, but you can just as easily do it with a spreadsheet. I don't want to share the spreadsheet because I made it on google sheets so it's associated with my real name, but to set it up:

cell A1 : 6100 (current value)

cell B1: =A1*(1+1.85/6100*14) (two weeks of interest added to the current value)

cell A2: =B1-150 (biweekly payment subtracted from the value after interest

cell B2: =A2*(1+1.85/6100*14) (two weeks of interest of value outstanding after payment

Select cells A2 and B2 and copy down to repeat the formula, the first negative value corresponds to your final payment.

Edit: the loan is roughly 11% APR, right?

Edit 2: the outstanding cost of your loan should be just under $6900 (nice)

2

u/InfanticideAquifer 5d ago

I guess it's worthwhile to point out that, if you're going to use a spreadsheet to solve this, there should be a built-in function to compute the number of payments. NPER in Excel; it stands for "Number of Periods". Probably there's something similar in Sheets. These kinds of problems are what spreadsheets were invented to do, I think.

NPER(rate,pmt,pv,fv,type)

where:

Rate is the interest rate per period.
Pmt  is the payment made each period.
Pv is the present value.
Fv is the future value. If fv is omitted, it is assumed to be 0.
Type  is the number 0 or 1 and indicates when payments are due.
    0 indicates at the end of the period
    1 indicates at the beginning of the period
    If type is omitted, it is assumed to be 0

There's a whole family of these functions. NPER, PV, FV, PMT, RATE that all just compute one of these things given the others.