Question

You had to pay $500 three months ago, $500 today and and $499.55 three month from today. if 12% simple intrest is charged when single payment of 1590 will settle debt ? Answer provide in months

Answer 1

Simple interest = P*r*n

where n = time in years, P = Principle and r = interest rate = 12% = 0.12

Amount After t years If we are considering Simple interest is P + simple interest = P + P*r*n = P(1 + r*n) -------------------(1)

We have to calculate amount that will be paid t Years from now that will settle all dept.

Amount of time at which we have to incur Simple interest on amount that we will have to pay 500 three months ago is t + 3

Amount of time at which we have to incur Simple interest on amount that we will have to pay 500 three months ago is t

Amount of time at which we have to incur Simple interest on amount that we will have to pay 499.55 three months ago is t - 3

Using Formula (1) Amount is given by:

A = 500(1 + 0.12(t + 3)) + 500(1 + 0.12(t)) + 499.55(1 + 0.12(t - 3))

This amount must equals 1590 that we have to pay t years from now in order to settle debt

=> A = 500(1 + 0.12(t + 3)) + 500(1 + 0.12(t)) + 499.55(1 + 0.12(t - 3)) = 1590

=> 500 + 60t + 180 + 500 + 60t + 499.55 + 59.946t - 179.838 = 1590

=> 1499.712 + 179.94600t = 1590

=> t = 0.501750525 Years

=> t = 0.501750525*12 = 6.02 months ~ 6 months(approx)

Hence, 12% simple interest is charged when single payment of 1590 will settle debt in 6 months

Hence The single payment of 1590 will settle debt in 6 month(approx)