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 at the end of each month for 10 years. Alternatively, under option B the employee receives a lump-sum payment equal to the present value of the payments described undeq option A.

Question

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 at the end of each month for 10 years. Alternatively, under option B the employee receives a lump-sum payment equal to the present value of the payments described undeq option A.

(a) find the sum of payments under option A.
(a) find the lump-sum payment under option B if it is determined by using an interest rate of 18% compounded monthly.

Answer 1

Option A=1575(120mo.)=189000.

Option B=189000(r+1)^n
r=(18/12)/100=0.015=MPR=monthly % rate
n=(10yr)(12)=120=number of compounding
periods.

Option B=189000(1.015)^120=1128000.

Answer 2

CORRECTION:

Option B = 1575(1.015)^120 = 9401.68

Answer 3

To find the sum of payments under option A, we need to determine the total amount that will be received over the 10-year period.

Since the employee will receive $1,575 at the end of each month for 10 years, we can calculate the monthly payments first.

$1,575 x 12 (months in a year) = $18,900 (annual payment)

Then, we can multiply the annual payment by the number of years to get the sum of payments:

$18,900 x 10 (years) = $189,000

So, under option A, the sum of payments is $189,000.

Now, let's move on to finding the lump-sum payment under option B using an interest rate of 18% compounded monthly.

To calculate the present value of the monthly payments, we need to use the present value formula, which is given by:

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

Where:
PV = Present Value
PMT = Payment (in this case, $1,575)
r = Interest rate per period (18% divided by 12 to convert to monthly rate)
n = Number of periods (10 years x 12 months)

Let's plug in the values and calculate:

r = 18% / 12 = 1.5% (monthly rate)
n = 10 years x 12 months = 120 months
PMT = $1,575

PV = $1,575 * [1 - (1 + 1.5%)^(-120)] / 1.5%

Using a calculator or spreadsheet, we can compute the present value as:

PV = $1,575 * [1 - (1 + 0.015)^(-120)] / 0.015

The resulting lump-sum payment under option B will be the present value calculated above.

Note: You can use financial calculators, spreadsheet programs (such as Excel), or online present value calculators to simplify the calculations.