Question12 Perpetual Insurance Co. is selling a perpetuity contract that pays $1,450 monthly. The contract currently sells for $65,000. (Do not round intermediate calculations. Round your answer to 2 decimal places.) A. What is the monthly return on this investment vehicle? Answer: [input]% per month B. What is the APR? Answer: [input]% C. What is the effective annual rate? Answer: [input]% Maximum marks: 3 Flag question undefined

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Question12 Perpetual Insurance Co. is selling a perpetuity contract that pays $1,450 monthly. The contract currently sells for $65,000. (Do not round intermediate calculations. Round your answer to 2 decimal places.) A. What is the monthly return on this investment vehicle? Answer: [input]% per month B. What is the APR? Answer: [input]% C. What is the effective annual rate? Answer: [input]% Maximum marks: 3 Flag question undefined [input]简答题

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BlackTom AI · Accepted Answer

Perpetuity valuation: Price = Payment / monthly rate, so monthly rate = Payment / Price.

1) Relevant concepts
- Perpetuity formula: P = C / r (with C = periodic payment, r = periodic rate).
- APR (nominal annual rate) = periodic rate × number of periods per year (no compounding).
- Effective annual rate (EAR) = (1 + r_period)^(periods per year) − 1 (captures compounding).

2) Step-by-step calculations
A. Monthly return (r_month)
- Payment C = $1,450; Price P = $65,000.
- r_month = C / P = 1,450 / 65,000.
- Compute: 1,450 ÷ 65,000 = 0.0223076923076923.
- As a percentage: 0.0223076923 × 100 = 2.23076923076923% → rounded to 2.23% per month.

B. APR (nominal annual percentage rate)
- APR = r_month × 12 = 0.0223076923076923 × 12 = 0.2676923076923076.
- As a percentage: 0.2676923076923076 × 100 = 26.76923076923076% → rounded to 26.77%.

C. Effective annual rate (EAR)
- EAR = (1 + r_month)^12 − 1 = (1.0223076923076923)^12 − 1.
- Compute with exponential expansion or a calculator:
  ln(1.0223076923) ≈ 0.0220626; 12·ln(...) ≈ 0.2647512;
  exp(0.2647512) ≈ 1.3031184.
- EAR = 1.3031184 − 1 = 0.3031184 → as a percentage 30.31184% → rounded to 30.31%.

3) Why these are correct
- The monthly rate directly follows from the perpetuity formula (price equals payment divided by rate). APR is simply twelve times the monthly rate (nominal, no compounding). EAR correctly compounds the monthly rate 12 times to reflect actual annual growth.

4) Common mistakes / why alternatives would be wrong
- Using APR as EAR (reporting 26.77% as effective) ignores monthly compounding and underestimates the annual return.
- Reversing price and payment (e.g., computing 65,000/1,450) would produce an incorrect tiny rate.
- Forgetting to convert to percentage or rounding too early can slightly distort results.

Conclusion: Monthly return = 2.23% per month; APR = 26.77%; EAR = 30.31%, which matches the provided answers.

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