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Capital recovery cost; interest on motorbike loan

Short answer

Capital recovery cost is the uniform annual amount to recover an asset's initial cost minus salvage over its life. Loan 1,40,000, monthly 10,000 for 20 months gives (P/A,i,20)=14; solving yields i ≈ 3.67% per month, nominal annual rate ≈ 44%.

Define 'Capital Recovery Cost'. Mr. Fox purchased a motorbike which cost Rs. 2,00,000. He pays 30% as down payment. Remaining amount will be paid on installment basis and he wishes to pay Rs. 10,000 per month for 20 months. What annual interest rate is he paying?

Capital recovery cost

Capital recovery (CR) cost is the equivalent uniform annual cost of owning an asset: the annual amount needed to recover the initial investment I over its life N at interest rate i, after allowing for the salvage value S.

CR = I (A/P, i, N) − S (A/F, i, N) = (I − S)(A/P, i, N) + S·i

It is the sum of annual depreciation and the interest on the unrecovered capital. It is a component of annual worth (AW) and of cost comparisons between alternatives.

Numerical

  • Down payment = 30% × 2,00,000 = Rs 60,000
  • Loan P = 2,00,000 − 60,000 = Rs 1,40,000
  • A = Rs 10,000 per month, n = 20 months
 +1,40,000
 0    1     2     ...     20     (months)
      ↓     ↓             ↓
    10,000 at the end of each month

Equation: 1,40,000 = 10,000 (P/A, i, 20), so (P/A, i, 20) = 14.

i per month(P/A, i, 20)vs 14
3.0%14.8775too high
4.0%13.5903too low
3.667%14.0000= 14

Interpolation: i = 3 + 1 × (14.8775 − 14)/(14.8775 − 13.5903) ≈ 3.67% per month.

  • Nominal annual rate = 12 × 3.667% = 44.0% per year
  • Effective annual rate = (1 + 0.03667)^12 − 1 = 54.1%

Answer: Mr. Fox pays about 44% per year nominal (≈ 54% effective). The rate is very high because Rs 2,00,000 is paid back for a Rs 1,40,000 loan within only 20 months.

✓ Answer checked by Claude Opus 5.5 (high effort)

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