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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?
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Appu retires at 60 years receiving a pension of 14,400 a year paid in ...
Calculation of Equivalent Single Sum for Appu's Pension


Given Information:


  • Appu retires at 60 years.

  • He receives a pension of 14,400 a year.

  • The pension is paid in half-yearly installments.

  • His life expectation is 13 years.

  • Interest at 4% nà is payable half-yearly.



Calculation of Present Value of Pension:

Present Value of an Annuity due = (PMT/i) x [1 - 1/(1+i)^n], where PMT is the periodic payment, i is the interest rate, and n is the number of periods.

As the pension is paid in half-yearly installments, n = 13 x 2 = 26.

Thus, Present Value of Pension = (14,400/0.04) x [1 - 1/(1.04)^26] = 220,249.82


Calculation of Equivalent Single Sum:

Equivalent Single Sum = Present Value of Pension + Present Value of Residual Interest

Present Value of Residual Interest = 14,400/(0.04 x 2) x (1 - 1/(1.04)^13) = 81,225.18

Thus, Equivalent Single Sum = 220,249.82 + 81,225.18 = 301,475


Explanation:

The equivalent single sum is the lump sum amount that would be required to generate the same cash flows as the pension payments over the given time period, taking into account the time value of money through the application of an appropriate discount rate. Here, we have calculated the present value of the pension payments and added to it the present value of residual interest, which is the interest earned on the remaining balance of the pension payments after the life expectation of the retiree. The sum of these two values gives us the equivalent single sum that would be required to generate the same cash flows as the pension payments.
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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?
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