Question

If you take out a car loan for $35,000, will pay an annual interest rate of 4% on the loan, and make monthly payments of $547.58, how many payments will you need to make? -What are you solving for? -What is your answer?

Answer 1

If loan amount is (P), rate of interest is (i), and EMI is known then number of payments can be calculated using below formula

n = [-log(1 - iP/EMI)/ log(1 + i)]

Where,

                  Loan amount (P) = $35000

                  EMI = $547.58

                  Interest rate (Monthly) = 0.33333333%

Lets put all the values in the formula

n = [ - log (1 - 0.0033333333* 35000/ 547.58)/ log(1 + 0.0033333333)]

    = [ - log (1 - 116.6666655/ 547.58)/ log(1.0033333333)]

    = [ - log (1 - 0.21306)/ log(1.0033333333)]

    = [ - log (0.78694)/ log(1.0033333333)]

Lets put the log values in the equation, the values could be found in log table or we can use calculator

    = [ - (-0.104058379028824)/ 0.00144524085975256]

    = 0.104058379028824/ 0.00144524085975256

    = 72

So total time it will take to pay off the loan is 72 Month

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Hope that helps.

Feel free to comment if you need further assistance J