Numerical answer
A loan is repaid in two equal annual instalments of ₹12,100 each, the first paid one year after the loan is taken. If interest is charged at 10% per annum compounded annually, what was the amount (in ₹) of the loan?
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Answer: 21000
The loan equals the present value of the instalments.
PV of first instalment = 12100/1.1 = 11,000.
PV of second instalment = 12100/1.1² = 12100/1.21 = 10,000.
Loan = 11,000 + 10,000 = ₹21,000.
Check: after year 1 the debt is 23,100; paying 12,100 leaves 11,000; after year 2 it is 12,100, cleared by the second instalment ✓.
PV of first instalment = 12100/1.1 = 11,000.
PV of second instalment = 12100/1.1² = 12100/1.21 = 10,000.
Loan = 11,000 + 10,000 = ₹21,000.
Check: after year 1 the debt is 23,100; paying 12,100 leaves 11,000; after year 2 it is 12,100, cleared by the second instalment ✓.
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