Calculate the monthly EMI on a loan from the amount borrowed, the annual interest rate and the number of months, with the total repaid and the total interest.
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A ₹1,00,000 loan at 12% a year for 12 months: R = 0.01, (1.01)¹² = 1.126825, EMI = 1,00,000 × 0.01 × 1.126825 ÷ 0.126825 = ₹8,884.88; total repaid ₹1,06,619, interest ₹6,619.
Step 1 — convert.
i = 9 ÷ 12 ÷ 100 = 0.0075
n = 5 × 12 = 60
Step 2 — the power term.
(1.0075)60 = 1.565681
Step 3 — substitute.
Numerator = 500 000 × 0.0075 × 1.565681 = 3750 × 1.565681 = 5871.30
Denominator = 1.565681 − 1 = 0.565681
EMI = 5871.30 ÷ 0.565681 = ₹10,379.18
Step 4 — the total cost.
Total paid = 10 379.18 × 60 = ₹6,22,750.70
Total interest = 6 22 750.70 − 5 00 000 = ₹1,22,750.70
Quoted from EMI Formula — How Banks Compute a Monthly Payment.
i = 0.0075, n = 120, (1.0075)120 = 2.4513571
Numerator = 3750 × 2.4513571 = 9192.59
Denominator = 2.4513571 − 1 = 1.4513571
EMI = 9192.59 ÷ 1.4513571 = ₹6,333.79
Total paid = 6333.79 × 120 = ₹7,60,054.64
Total interest = ₹2,60,054.64
Quoted from EMI Formula — How Banks Compute a Monthly Payment.
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