you have a loan for $150,000 @ 5% on a 30 yr mortgage. You plan to pay off your loan in 10 yrs, Do you want your loan to be figured using the "Rule of 78" or the "Unpaid Principal Balance Rule" please help if possible Thanks in advanced
From the method Reiny has supplied, which applies to equal payments for 30 years, where r=5%/12=0.0041666...
150000(1+r)^360=Payment*[(1+r)^360-1]/r
or
Monthly Payment = $805.23
The rule of 78 assumes the borrower owes all the interest at the start, so together with the principal, the borrower owes:
805.23*360=$289883.68
meaning the finance charges are
$289883.68-150000=139883.68 over 360 payments.
The finance charge (fixed interest charge) is subdivided into 360 unit for the first month, 359 units for the second, .... 1 unit for the last month for a total of 64980 units.
So if the loan is prepaid after 10 years, the "refund" of the interest is the number of units left for the next 20 years, 1+2+...+240=28920 units, or
$139883*(28920)/64980=62256.63
So the borrower will have to pay, after 10 years of monthly payments of 805.23, the remaining principal of 100000 + remaining interest of 139883.68-62256.63
=77627.05 for a total of 177627.05 to pay off the mortgage.
So the borrower will have paid
120*805.23+100000+77627.05
=274254.65
for the initial borrowed sum of 150000 (instead of 289883.68 if he had paid over 30 years).
This method of calculation was to simplify calculations before calculators and computers were available, and benefits the lender by penalizing pre-payments, and also making the borrower owe all the interest (called finance charges) as soon as the load is made. According to Wikipedia, this method of calculation is prohibited in the US for mortgages and loans over 61 months.
The unpaid principal balance is a fair method by which all payments are applied to the current interest, and the remainder to reduce the principal.
The amount remaining to pay off the mortgage after 10 years would be (r=0.004166...)
150000(1+r)^120-(805.2324342)((1+r)^120-1)/r
=122013.10
This is considerably less than the rule of 78.
To determine which method to use for calculating your loan payoff, it's important to understand both the "Rule of 78" and the "Unpaid Principal Balance Rule." Here's an explanation of both methods:
1. Rule of 78: The Rule of 78 is a method used to allocate the interest charges of a loan over its duration. Under this method, the total interest for the loan is divided into 12 equal parts (assuming monthly payments), with a greater proportion of the interest being paid in the earlier months. This method tends to benefit the lender more if you plan to pay off the loan early.
2. Unpaid Principal Balance Rule: The Unpaid Principal Balance (UPB) Rule, on the other hand, calculates the payoff amount based on the remaining principal balance on the loan. With this method, you would only pay interest on the actual outstanding balance, reducing the overall interest paid as you pay off the loan early.
Considering that you plan to pay off your loan in 10 years, it would usually be more beneficial to use the Unpaid Principal Balance Rule. This method allows you to save on interest costs because the interest charges are based on the remaining balance, which decreases over time as you make monthly payments.
It's important to note that different lenders may have their own policies and methods for calculating loan payoffs, so it's recommended to reach out to your lender or loan provider to confirm the specific rules they follow.
To determine whether you want your loan to be figured using the "Rule of 78" or the "Unpaid Principal Balance Rule," let's first understand what each rule entails.
1. Rule of 78:
The Rule of 78 is a method of calculating the interest due on a loan when it is paid off before the end of its term. Under the Rule of 78, the interest is calculated by allocating a higher proportion of the total interest cost to the earlier payments of the loan. This means that if you pay off your loan early, you may end up paying more interest than if you had used the Unpaid Principal Balance Rule.
2. Unpaid Principal Balance Rule:
The Unpaid Principal Balance Rule, also known as the Simple Interest Rule, is a method of calculating the interest due on a loan by considering the outstanding principal balance remaining at each payment period. This method calculates interest based on the amount of money you owe at each point in time. If you pay off your loan early using this rule, you will pay less interest compared to the Rule of 78.
In your case, you plan to pay off the loan in 10 years instead of the full 30-year term. Considering that you want to minimize the amount of interest paid, it would be more beneficial for you to use the Unpaid Principal Balance Rule. This rule calculates interest based on the remaining principal balance at each payment period, ensuring that you are charged only for the outstanding amount on the loan.
To calculate the repayments using the Unpaid Principal Balance Rule, you can follow these steps:
1. Determine the monthly interest rate: Divide the annual interest rate (5% in this case) by 12 to get the monthly interest rate in decimal form. In this case, the monthly interest rate is 0.05 / 12 = 0.0042.
2. Calculate the number of payments: Multiply the number of years you want to pay off the loan (10) by 12, as there are 12 months in a year. In this case, the number of payments is 10 * 12 = 120.
3. Use a loan amortization calculator or an Excel spreadsheet to determine the monthly payment amount that will allow you to pay off the loan in 10 years using the Unpaid Principal Balance Rule.
By using the Unpaid Principal Balance Rule, you will save on the amount of interest paid compared to the Rule of 78.