Question

Q.5 You have borrowed $24,000 and agreed to pay back the loan with monthly payments of $200. If the interest rate is 12%,how long will it take you to pay back the loan?

Answer 1

The formula for calculating the monthly equalised installments is.

[P x R x (1+R)^N]/[(1+R)^N-1], where P stands for the loan amount or principal, R is the interest rate per month.

Given the interest rate for 1 year is 12% hence the monthly interest rate is 12/12 = 1%

Hence let us substitute all the given data in the question in the above formula.

(24,000 * 0.01 * (1.01)ⁿ)/((1,01)ⁿ-1) = 200

240 * (1.01)ⁿ)/((1,01)ⁿ-1) =200

(1.01)ⁿ) * (240) = 200* ((1,01)ⁿ-1))

(1.01)ⁿ) * 40 = -200

(1.01)ⁿ = -5

Yes we were stuck ....!!

Let me tell you the reason why we can't calculate this along with a reason for the same.

When ever you take a loan you have to be in a position to at least pay the interest on the loan .

Here we are unable to make the interest payment itself on the loan and interest will go on accumulating.

Let me make a amortization schedule for you how it works.

Month	Opening Loan	Interest @ 1%	Monthly Installment	Closing Loan
1	24,000.00	240.00	200.00	24,040.00
2	24,040.00	240.40	200.00	24,080.40
3	24,080.40	240.80	200.00	24,121.20
4	24,121.20	241.21	200.00	24,162.42
5	24,162.42	241.62	200.00	24,204.04
6	24,204.04	242.04	200.00	24,246.08
7	24,246.08	242.46	200.00	24,288.54
8	24,288.54	242.89	200.00	24,331.43
9	24,331.43	243.31	200.00	24,374.74
10	24,374.74	243.75	200.00	24,418.49
11	24,418.49	244.18	200.00	24,462.67
12	24,462.67	244.63	200.00	24,507.30

You got it as soon as we come at the end of year -1 our balance is increasing

Hence our monthly emi should be alteast some amount greater than the first month interest