# Mathematics

Suppose an employee of a company is retiring and has the choice of two benefit options under the company pension plan. Option A consists of a guaranteed payment of \$1,575,000 at the end of each month for 10 years. Altematively, under option B the employee receives a lump-sum payment equal to the present value of the payments described under option A.
(a) find the sum of the payments under option A.
(b) find the lump-sum payment under option B if it is determined by using an interest rate of 18% compounded monthly.

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1. The monthly payment seems a little high for today's living standards.

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2. a. Option A.1575000 *120mo.=189000000 in 10 yrs.

b. Option B.1.575M @ 18% APR,Compounded
monthly. Pt=Po*(r+1)^n.
Pt=Value at 10 yrs. r=MPR=Monthly percentage rate. n=the number of
interest compounding periods.

r=18/12/100=0.015
n=12*10=120

Pt=1575000*(0.015+1)^120=9401683.52=
Value @ 10yrs.

Evidently, this is not a practical
situation.

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3. 1575000(12mnth*10years)=189,000,000

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