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medium30 ptsfintechmathsimulation

Loan EMI Schedule

A lending app shows borrowers a month-by-month repayment table. Let round2(x) = Math.round(x * 100) / 100 and r = annualRatePercent / 12 / 100.

The monthly instalment is emi = round2(principal * r * (1 + r)^months / ((1 + r)^months - 1)), or round2(principal / months) when r is 0.

Start with balance = principal. For each month m from 1 to months: interest = round2(balance * r). In every month except the last, principalPart = round2(emi - interest) and payment = emi. In the last month the borrower clears whatever is left: principalPart = balance and payment = round2(principalPart + interest). Then balance = round2(balance - principalPart).

Return one row per month: { month, payment, interest, principal, balance } where principal is principalPart and balance is the balance after the payment.

Example 1

Input: principal = 10000, annualRatePercent = 12, months = 3
Output: [{"month":1,"payment":3400.22,"interest":100,"principal":3300.22,"balance":6699.78},{"month":2,"payment":3400.22,"interest":67,"principal":3333.22,"balance":3366.56},{"month":3,"payment":3400.23,"interest":33.67,"principal":3366.56,"balance":0}]
Explanation: emi = 3400.22; the last row pays one extra paisa to clear the balance.

Example 2

Input: principal = 1200, annualRatePercent = 0, months = 4
Output: [{"month":1,"payment":300,"interest":0,"principal":300,"balance":900},{"month":2,"payment":300,"interest":0,"principal":300,"balance":600},{"month":3,"payment":300,"interest":0,"principal":300,"balance":300},{"month":4,"payment":300,"interest":0,"principal":300,"balance":0}]

Constraints

  • 1 <= principal <= 10^8
  • 0 <= annualRatePercent <= 36
  • 1 <= months <= 360
Hint 1

Follow the rounding steps literally; rounding at each step is what real lenders do.

Hint 2

The final month absorbs the rounding drift so the balance ends at exactly 0.

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