Overview
An equated monthly instalment(EMI) is a fixed payment amount made by a borrower to a lender at a specified date each calendar month.
Equated monthly installments are used to pay off both interest and principal each month so that over a specified number of years, the loan is paid off in full.
Note about equated monthly instalment
1. An equated monthly instalment (EMI) is a fixed payment made by a borrower to a lender on a specified date of each month.
2. EMIs allow borrowers the peace of mind of knowing exactly how much money they will need to pay each month toward their loan.
3. We can calculate EMI in two ways: the flat-rate method or the reducing-balance method.
We can calculate EMI flat-rate formula by adding together the principal loan amount and the interest on the principal and dividing the result by the number of periods multiply by the number of months.
The EMI reducing-balance method is calculated using the formula shown below, in which P is the principal amount borrowed, I is the annual interest rate, r is the periodic monthly interest rate, n is the total number of monthly payments, and t is the number of months in a year.
Solved examples
Example: A man buys a machine for Rs.20,00. What its value be after 6 years, if it is assumed to depreciate at a fixed rate of 12% per annum.
Sol.
Here we have P = 20,000, n = 6 and r = -0.12 (rate of interest is negative in depreciation)
Then,
So that the value of the machine in 6 years will be = 9288.08
Example: A machine valued at 500,000 depreciates at 6% per annum then in how many year its value will reduce to 100,000?
Sol. Here P = 500,000, r = 0.06, n = ? and the final value is = 100,000
We know that-
Taking log on both sides-
So that
Therefore approximately it will take 26 years for the value decline to 100,000
Example: Ayesha invests Rs. 3000 initially and then Rs. 1800 at the end of the first, second and third years and finally Rs. 600 at the end of 4th year.
If Ayesha pays the interest annually at the rate of 6.5% then find the value of the investment at the end of 5th year.
Sol.
Ayesha invests Rs. 3000 for 5 years and grows to-
The three sums of Rs. 1800 invests for 4, 3 and 2 years and grow in total-
And Rs. 600 invests for 1 year and grows to-
Then the total value at the end of 5 years will be 11,280.81
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