A compound interest tradeoffs calculator.
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README.md

A simple mortgage calculator, useful for finding a balance between paying off debpt early vs. investing early. Since calculations like this depend on a lot of unknowable variables (e.g., future interest rate of investments), it's only really useful as a handy way of getting a feel for compound interest tradeoffs.

The goal is to answer the question, "Is it better to pay off my debt early or should I put that money into an investment right now?"

Formulas

Monthly Debt Payment

Given a debt with a particular interest rate paid down monthly, how big will the monthly payment have to be in order to pay off the debt?

The Monthly Debt Payment algorithm uses the PMT formula. In plain English:

Loan * ((Monthly Interest * (1 + Monthly Interest) ^ Term in Months) / (((1 + Monthly Interest) ^ Term in Months) - 1))

How it looks in a spreadsheet app:

PMT(rate, number_of_periods, present_value, [future_value], [end_or_beginning])

Months to Payment Completion

Given a debt with a particular interest rate, how long will it take to finish paying it off if I pay the given amount?

Months to payment completion algorithm use the NPER formula. In plain English:

-LOG( 1 - ( Monthly Interest * ( Loan / Monthly Payment )), 2) / LOG(1 + Monthly Interest, 2)

And in an app:

NPER(rate, payment_amount, present_value)

Compound Interest With Monthly Contributions

How large will an investment be after a particular number of months at the given interest rate if I add a constant amount to it each month.

The Compound Interest With Monthly Contributions algorithm uses the FV ("Future Value") formula. Plain English:

X = B * (1 + i) ^ n + A * (((1 + i) ^ n - 1) / i)

Where:

B = initial balance
i = interest rate
A = monthly deposit
n = months of investment
X = final value of investment

And in the app:

FV(rate, number_of_periods, payment_amount, present_value, end_or_beginning)

Where:

rate
  The interest rate.
number_of_periods
  The number of payments to be made.
payment_amount
  The amount per period to be paid.
present_value
  The current value of the annuity.
end_or_beginning - [optional]
  Whether payments are due at the end (0) or beginning (1) of
  each period.
  • Adam Bachman, 2016