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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?
  • a)
    145000
  • b)
    144900
  • c)
    144800
  • d)
    144700
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Appu retires at 60 years receiving a pension of 14400 a year paid in h...
Given:
- Appu retires at 60 years
- He receives a pension of 14400 a year paid in half-yearly installments for the rest of his life
- His life expectation is 13 years
- Interest at 4% p.a. is payable half-yearly

To find:
- The single sum that is equivalent to his pension

Solution:

Step 1: Calculate the present value of each half-yearly installment of pension

Using the formula for present value of an annuity, we can calculate the present value of each half-yearly installment of pension as:

PV = PMT * [(1 - (1 + r)^(-n)) / r]

Where:
- PV is the present value
- PMT is the payment per period (i.e. half-yearly pension installment)
- r is the interest rate per period (i.e. half-yearly interest rate)
- n is the total number of periods (i.e. number of half-years Appu is expected to receive pension)

Substituting the given values, we get:

PV = 7200 * [(1 - (1 + 0.04/2)^(-13*2)) / (0.04/2)]
PV = 7200 * [(1 - 0.5084) / 0.02]
PV = 7200 * 24.08
PV = 173376

Therefore, the present value of each half-yearly installment of pension is 173376.

Step 2: Calculate the equivalent single sum

Using the formula for present value of a single sum, we can calculate the equivalent single sum as:

PV = FV / (1 + r)^n

Where:
- PV is the present value (which we want to find)
- FV is the future value (i.e. the total amount of pension Appu will receive over 13 years)
- r is the interest rate per period (i.e. half-yearly interest rate)
- n is the total number of periods (i.e. number of half-years Appu is expected to receive pension)

Substituting the given values, we get:

PV = 14400 * 2 * [(1 - (1 + 0.04/2)^(-13*2)) / (0.04/2)] / (1 + 0.04/2)^13
PV = 28800 * 24.08 / 1.602
PV = 144900

Therefore, the equivalent single sum is 144900.

Hence, the correct option is B) 144900.
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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?a)145000b)144900c)144800d)144700Correct answer is option 'B'. Can you explain this answer?
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