Question

Jessica owes $2550 on a credit card that charges 1.7% effective interest per month. She decides to pay off the debt by making monthly payments of $70, starting one month from now, followed by a final smaller payment. How many payments, including the final one, will be required?

Answer = payments. (3 decimal place)

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) = $2550

                  EMI = $70

                  Interest rate (Monthly) = 1.7%

Lets put all the values in the formula

n = [ - log (1 - 0.017* 2550/ 70)/ log(1 + 0.017)]

    = [ - log (1 - 43.35/ 70)/ log(1.017)]

    = [ - log (1 - 0.61929)/ log(1.017)]

    = [ - log (0.38071)/ log(1.017)]

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

    = [ - (-0.419405715547647)/ 0.00732095292274456]

    = 0.419405715547647/ 0.00732095292274456

    = 57.29

So total time it will take to pay off the loan is 57 month

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