On problem set 1, problem 2, he gives this equation to compute what payments are necessary to pay off debt in a year:
"Monthly interest rate = Annual interest rate / 12.0
Updated balance each month = Previous balance * (1 + Monthly interest rate) – Minimum monthly payment"
Why does he have "(1 + Monthly interest rate)" and what is the "1" supposed to be/do?
MIT 6.00 Intro Computer Science (OCW)
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It's the correct formula because it happens to work, but to see that it does consider this:
You have a current balance of $100 and you pay 5% per month interest. You want to know next month's balance after interest. You take 5% of $100 and add it to the $100. So, $100 + .05*$100.
However, you could also take 1.05*$100 and get the same answer. The "1" has the effect of copying the original balance while the .05 has the effect of adding the interest.
It turns out that it's easier to work with the formula in this form (compared to a form that works by adding), especially when you start compounding over multiple periods.
it is a different way of expressing:
previous balance + (previous balance * Monthly interest rate)
It is a "simplified" expression for calculating an "updated balance each month", lets call "UB" to make it shorter. The "UB" is comprised of several parts:
1. You Previous_balance - amount you already owe to the bank, let's call it ( PB )
2. plus (+) The "Accumulated Interest" - amount that adds to your debt each month
3. minus (-) "Minimum monthly payment" - amount you pay to the bank to reduce and eventually to pay off your debt.
UB = PB * (1 + Monthly interest rate) – Minimum monthly payment" =
hint: multiply PB over ( 1 + Monthly interest rate )
= PB + PB * "Monthly Interest rate" - "Minimum monthly payment" or by using plain English
Updated Balance is a sum of the Previous Balance and Monthly Interest minus you Minimum monthly payment.
I hope it helps.