Financial Calculations Demonstrating the Various
Speeds of Paying Off Debt:
Link to
Financial Calculations Demonstrating the Various Speeds of
Paying Off Debt Using Python, class files
We first used the formula:
- Any payment you make at beginning of month is deducted
from balance = p0.
- At beginning of month 1, credit company charges
interest on balance.
- So if your annual interest rate is r, at the beginning
of month 1,your new balance is your previous balance b0
less the payment p0 plus interest on the new balance for the
month. "b1 = (b0-p0) * (1 +r/12)".
- In month 1, we make another payment p1 to cover
interest costs too, thus at beginning of month 2,
balance is: "b2 = (b1-p1) * (1 + r/12)".
- We saw that if you choose to pay off the minimum
monthly payment each month, compound interest
dramatically reduces your ability to lower your
debt.
Next, we calculated the minimum fixed monthly payment
needed in order to pay off a credit card balance within
12 months.
- So in this part, we are not dealing with a
minimum monthly payment rate.
- We computed the lowest monthly payment that would pay
off the debt in under 1 year.
- We assumed interest was compounded monthly
according to the balance at the end of the month after
payment was made.
- Monthly Interest Rate = "Annual Interest Rate / 12" .
- Updated balance each month = "(Previous balance - Minimum monthly payment) * (1 +
Monthly Interest Rate)".
We then used bisection search to make our program
faster.
- Lower bound = 1/12th of original balance.
- Upper bound = 1/12th of the balance
- After it has been compounded monthly for an entire year
= "(Balance * (1 + Monthly interest rate) ** 12) / 12".
- You should get the same answer as you did for part 2 in
this part 3 only faster with bisection search.
