Refinancing Decision

Refinancing Decision.carbide.md

Refinancing Decision

This Gist was automatically created by Carbide, a free online programming environment.

You can view a live, interactive version of this Gist here.

refinancing.js

function AnnuityValue(R,T){ return (1/R) * (1 - 1/((1+R)**T)); }

/// ################################
/// ################################

var InitialBalance = 500; ///++InitialBalance:++ **Amount you borrow** from the bank (in $1000s).
var R = 0.06/12; ///++R:++ Monthly **mortgage rate** when you take out the mortggae.
var T = 30*12; ///++T:++ **How long** it takes **until you to pay off principal** you owe if you keep on making the **same monthly payments**? a.k.a., amortization period.
var A = AnnuityValue(R,T); ///++A:++ **Present value** of a **T-month $1 annuity** if the **monthly interest rate is R**.
var MonthlyPayment = InitialBalance/A; ///++MonthlyPayment:++ **Amount you pay** each month (in $1000s) for **next T months** if you **borrow InitialBalance** from the bank when the monthly **mortgage rate is R**.

/// ################################
/// ################################

var RemainingT = 10*12; ///++RemainingT:++ **Number of months left** on mortgage.
var RemainingA = AnnuityValue(R,RemainingT); ///++RemainingA:++ **Present value** of a **RemainingT-month $1 annuity** if the **monthly interest rate is R**.
var RemainingPaymentsPV = MonthlyPayment * RemainingA; ///++RemainingPaymentsPV:++ **Present value** of your **remaining monthly payments** for the **next RemainingT months** if the **mortgage rate is R** (in $1000s).

/// ################################
/// ################################

var NewR = 0.054/12; ///++NewR:++ **New mortgage rate** that suddenly comes into effect **as of RemainingT months left** in your loan.
var NewRemainingA = AnnuityValue(NewR,RemainingT); ///++NewRemainingA:++ **Present value** of a **RemainingT-month $1 annuity** if the **monthly interest rate is NewR**.
var NewRemainingPaymentsPV = NewRemainingA * MonthlyPayment; ///++NewRemainingPaymentsPV:++ **Present value** of your **remaining monthly payments** for the **next RemainingT months** if the **mortgage rate is NewR** (in $1000s).



var MonthlyPaymentIfRefi = RemainingPaymentsPV / NewRemainingA; ///++MonthlyPaymentIfRefi:++ **Amount you would pay** each month (in $1000s) **if you refinance at NewR**.
/// ################################
/// ################################

var PrepaymentPenalty = 0.02; ///++PrepaymentPenalty:++ **Fraction of remaining balance** that **you pay** as fee to the bank **if you refinance**.
var CostOfPrepayment  = PrepaymentPenalty * RemainingPaymentsPV; ///++CostOfPrepayment:++ **Amount of money** (in $1000s) that **you pay** as fee to the bank **if you refinance**.
var CostOfRateChange  = (NewRemainingPaymentsPV - RemainingPaymentsPV); ///++CostOfRateChange:++ **Increase in present value of monthly payments** you still owe to the bank **due to mortgage rate change**.
if (CostOfRateChange > CostOfPrepayment){ ///**Question:** Should you refinance?
    var Decision = 'Refinance';
} else {
    var Decision = 'Wait';
}	
Decision