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DO NOT USE EXCEL. PLEASE SHOW STEP BY STEP. Maria purchased an immediate annuity from...

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Finance

DO NOT USE EXCEL. PLEASE SHOW STEP BY STEP.

Maria purchased an immediate annuity from an insurance company. The annuity will be paid out at $10,000 per year for 15 years. Insurance companies invest premiums in fixed-rate bonds, which can be redeemed at face value within 9 years. It pays coupons at an annual interest rate of 6% at the end of each year.

(i) Calculate the duration of the annuity at an interest rate of 5% per annum effective.

(ii) Calculate the duration of the bond at an interest rate of 5% per annum effective.

(iii) Explain whether the insurance company will make a profit or a loss if interest rates increase slightly at all terms.

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