Appu retires at 60 years receiving a pension of 14400, a year paid in half yearly installments for rest of his life after recknowing his life expectations to be 13 years and that interest at 4%p.a. is payable half yearly. (A) 1,45,000 (B) 1,44,900 (C) 1,44,800 (D) 1,44,700 Answer is (B) , but please explain the answer?

Question

Answer

Calculation of the present value of the pension:
To calculate the present value of the pension, we need to determine the amount that Appu would receive every six months for the next 13 years. The interest is payable semi-annually at a rate of 4% per annum.

Step 1: Determine the half-yearly pension amount:
The annual pension amount is given as 14,400. To find the half-yearly amount, we divide it by 2:
Half-yearly pension = 14,400 / 2 = 7,200

Step 2: Determine the number of periods:
The pension is paid for the next 13 years. Since interest is payable semi-annually, the number of periods would be 13 * 2 = 26.

Step 3: Determine the discount rate:
The interest rate is given as 4% per annum, payable semi-annually. To find the discount rate for each period, we divide the annual interest rate by the number of periods in a year:
Discount rate per period = 4% / 2 = 2%

Step 4: Calculate the present value:
Using the formula for the present value of an annuity, we can calculate the present value of the pension:
Present value = (Half-yearly pension * (1 - (1 + discount rate)^-number of periods)) / discount rate

Substituting the values:
Present value = (7,200 * (1 - (1 + 0.02)^-26)) / 0.02
Present value ≈ 144,900

Therefore, the present value of the pension is approximately 144,900.

Conclusion:
The present value of the pension is calculated to be approximately 144,900. Therefore, the correct answer is (B) 1,44,900.

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Appu retires at 60 years receiving a pension of 14,400 a year paid in half-yearly installmentsfor rest of his life after reckoning his life expectation to be 13 years and that interest at 4%p.a. is payable half-yearly. What single sum is equivalent to his pension?(

Appu retires at 60 years receiving a pension of 14400 a year paid in half-yearly installments for rest of his life after reckoning his life expectation to be 13 years and that interest at 4% p.a. is payable half-yearly. What single sum is equivalent to his pension?

Appu retires at 60 years receiving a pension of 14,400 a year paid in half-yearly installments for rest of his life after reckoning his life expectation to be 13 years and that interest at 4% pa is payable half-yearly. What single sum is equivalent to his pension?

Appu retires at 60 years receiving a pension of 14,400 a year paid in half-yearly installments for rest of his life after reckoning his life expectation to be 13 years and that interest at 4% nà is payable half-yearly. What single sum is equivalent to his pension?

Appu retires at 60 years receiving a pension of 14,400 a year paid in half-yearly installments for rest of his life after reckoning his life expectation to be 13 years and that interest at 4% pa is payable half-yearly?

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