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Direct Ratio Formula
316
Problem
Find the interest rate on a loan of 230000 , the loan is repaid with installments of 60000 , every six months for 2years.
Direct Ratio Method
Direct Ratio Formula
Solution
Given
j
=
dr
0.034482758 x 100
3.45% compounded semi-annually
A= 230000
R= 60000
m= 2
t= 2
n= 4
Amortization
Schedule
Principle Payment Interest To Principal New Balance
1. 2000.00 172.13 10.00 162.13 1837.87
2. 1837.87 172.13 9.19 162.94 1674.93
3. 1674.93 172.13 8.37 163.76 1511.17
4. 1511.17 172.13 7.56 164.57 1346.60
5. 1346.60 172.13 6.73 165.40 1181.20
6. 1181.20 172.13 5.91 166.22 1014.98
7. 1014.20 172.13 5.07 167.06 847.92
8. 847.92 172.13 4.24 167.89 680.03
9. 680.03 172.13 3.40 168.73 511.30
10. 511.30 172.13 2.56 169.57 341.73
11. 341.73 172.13 1.71 170.42 171.31
12. 171.31 172.17 .86 171.31 -0-
Nominal Rate
Effective rate
Solution
j
=
i
Direct Ratio Method
dr
j
=
dr
2mI
--------------------
A(n+1)+ 1/3I(n-1)
2I
---------------------
A(n+1)+ 1/3I(n-1)
2mI
------------------
A(n+1)+ 1/3I(n-1)
And
I=nR-A
I=(4)(60000)-230000
I= 10000
2(2)(10000)
-------------------------------
(230000)(5)+1/3(10000)(3)
The direct ratio method takes into consideration the fact that you pay more interest in the beginning of a loan, and pay less and less interest as the debt is reduced.
However...
In case you pay off early, the refund of interest will be according to the direct ratio method. Here’s what that means. Since the loan was for 12 months, add the numbers from
1 – 12 (a little math). Now, 1 + 2 + … + 12 = 78.
Rule of 78
Direct Ratio Method
When paying off a loan, the repayments consist of two parts: the principal and the interest charge. The direct ratio method weights earlier payments with more interest than later ones. If the loan is not terminated or prepaid early, the total interest paid between simple interest and the direct ratio method will be equal.
Direct ratio method is often called the rule of 78; the Rule of 78 is a term used in lending that refers to a method of yearly interest calculation.
Direct Ratio Method
Uses an approximate division into principal and interest. Another method used for calculating the unknown rate of interest on installment loans.