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Advanced Math/Interest Rate Formula
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Question
I would like to know what the formula is to find out what interest rate is on an automobile loan if I only know the amount of the loan, the term in months & the monthly payments.
I know to calculate the payments I could use this formula:
P ( r / 12 )
-------------------------
-m
(1 - ( 1 + r / 12 ) )
But I need a formula to calculate the RATE.
Any help would be great
Tye
Given P and A, we have (r/12)/(1-(1+r/12)^-m)=A/P. I assume the number of months, m, is known as well. To get r, put these values in a spreadsheet and use successive approximation to get as close as you want. Note that on some loans, there is a special fee every month that is added on as well.
Put the entire formula in and the known values in several cells in the first row. Copy this down to the second row. In the column for i, the interest rate, put in values that are high and low, like 0 and 0.3.
In the third row, put in the same numbers except make the interest rate in this third row the average of the interest rates in the first two rows.
Decide whether to copy the value from the third row to the first row or the second row depending on which side the answer is on. Input into the new interest rate the average of the last two interest rates where one was high and one was low.
I wish I could mail you the answer, but what I did was this.
In column A, I input the base amount.
In column B, I input the interest rate.
In column C, I input =B#/12, where # is which row we are in.
In column D, I input the number of years.
In column E, I input the total months, =12*D#.
In column F, I input the final amount, A#((1+C#)^E#-1)/C#.
I copied these formulas down, changing only column B. Most of the time it was the last two rows over 2, but sometimes it was the last row and two rows before over 2. It depends on finding values in column F that are high and low.
If the values in column F are both high or both low, adjust one of the initial interest rates until one is high and one is low.
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Scott A Wilson
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