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.
The monthly payment seems a little high for today's living standards.
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.
1575000(12mnth*10years)=189,000,000
To find the sum of the payments under option A, we need to multiply the guaranteed payment amount of $1,575,000 by the total number of payments over the 10-year period.
(a) Calculation for sum of payments under option A:
Number of payments = 12 (months in a year) * 10 (years) = 120
Sum of payments = $1,575,000 * 120 = $189,000,000
Therefore, the sum of the payments under option A is $189,000,000.
To find the lump-sum payment under option B, we need to calculate the present value of the payments under option A using the given interest rate of 18% compounded monthly.
(b) Calculation for lump-sum payment under option B:
Present Value (PV) = Payment / (1 + r)^n
Where:
PV = Present Value of the lump-sum payment
Payment = Monthly payment of $1,575,000
r = Interest rate per period (18% divided by 12 months)
n = Total number of periods (120 months)
r = 18% / 12 = 1.5% or 0.015 (in decimal)
n = 120
Using the formula, we can calculate the present value:
PV = $1,575,000 / (1 + 0.015)^120
PV ≈ $1,575,000 / (1.015)^120
PV ≈ $1,575,000 / 1.74742206
Calculating this value gives us approximately:
PV ≈ $900,850.11
Therefore, the lump-sum payment under option B, determined by using an interest rate of 18% compounded monthly, is approximately $900,850.11.