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Early Retirement – Lump Sum vs. Payments










































Lump Sum vs. Payments

There is an early retirement plan offered by a MNC.

   • There are two options for each employee to opt for early retirement.

             - The staff can receive quarterly payment of RM800 each for 3 years, with the first payment made in the first quarter from now

             - or a lump sum from today.

Assuming an interest rate of 6% compounded quarterly, what is the lump sum today (present value) that would equal the sum of the future payments to be made?

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Oct 01, 2012
Lump Sum vs. Payments
by: Staff


Answer:


Part I

Present value of stream of future payments.





Math – graph of present value of 3 year annuity






      Definitions:


                   PV = present value of future payments


                   A = individual payments


                   i = interest rate (also called the discount rate)


                   n = number of payment periods


      The Present Value of an Annuity can be calculated as follows:

                   PV = (A/i)*[1 - (1/(1+i)ⁿ]

      Values Assigned to Variables:


                   PV = unknown

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Oct 01, 2012
Lump Sum vs. Payments
by: Staff


--------------------------------------------------
Part II

                   A = RM800 per quarter

                   i = interest rate of 6% compounded quarterly = .06 per year / 4 quarters per year = 0.015 per quarter

                   n = 3 years * 4 quarters per year = 12 payment periods


      The Final Equation:

                   PV = (A/i)*[1 - (1/(1+i)ⁿ]

                   PV = (800/0.015)*[1 - (1/(1+0.015)¹²]


      The Calculations:

                   PV = (800/0.015)*[1 - (1/(1+0.015)¹²]

                   PV = (800/0.015)*[1 - (1/(1.015)¹²]

                   PV = (800/0.015)*[1 - (1/1.1956181714615)]

                   PV = (800/0.015)*[1 - 0.8363874218954]

                   PV = (800/0.015)*(0.1636125781046)

                   PV = 8726.0041655786663



Final Answer:


                 Present Value of all future payments = RM8726.00

Thanks for writing.

Staff
www.solving-math-problems.com


Oct 22, 2012
n value
by: Anonymous

I would like to check if n = 12 months x 3 years/4 quarters? This is because it says the first payment was made in the first quarter which means 1 year, it was paid 3 times, right?

Therefore n = 9?

Oct 22, 2012
Using Geometric (GP) Formula
by: Anonymous

How do you used GP formula to do this maths? Can you please show me?

Thanks

Oct 22, 2012
Number of time periods
by: Staff


Answer II:

Unless otherwise stated, payments from annuities are assumed to be made at the end of each time period.

Fortunately, the problem statement is specific. It does not leave any doubt: “the first payment made in the first quarter from now.

In other words, the first payment will be made 3 months from now, at the end of the quarter (the quarter which begins now).

This type of payment is called “in arrears”. Payment “in arrears” means that payment is made after some service has been provided. In the case of an annuity, the money is left in an interest bearing account (or investment) for the entire payment period so that interest can be earned on the money.

In general, mortgage payments are made “in arrears”, employee salaries are paid “in arrears”, dividends are paid “in arrears”, and annuities are usually paid “in arrears” (you may be given the option of being paid at the beginning of the time period).

If the payment is made at the beginning of a payment period it is called “in advance”.

Rent is usually paid “in advance”. Pensions are often paid “in advance”. ½ of Real Property Tax in California is paid in advance, and ½ is paid “in arrears”.

n = 12 months x 3 years/(3 months per quarter ) = 12 quarters



Thanks for writing.

Staff
www.solving-math-problems.com


Oct 22, 2012
Geometric Progression (GP)
by: Staff

Answer III:

The formula used to calculate the present value of an annuity is based on the Geometric Progression (GP) formula:

A = PV*(1 + i)n

A = single, future payment to you (final balance in a savings account)
PV = present value of principle (the initial deposit in the bank)
i = decimal form of annual interest rate
n = time periods

To determine the “present value of a SINGLE future payment”, solve for P (just divide each side of the equation by (1 + i)n):

A*(1 + i)-n = PV

PV = A*(1 + i)-n

Since you have a series of single payments, you must use this formula to calculate the present value for each individual payment, and then add them up.

That’s the idea, but there is a single formula that does it all. This is the formula that you should use for this problem:


PV = (A/i)*[1 - (1/(1+i)ⁿ]


PV = present value of all future payments


A = individual payments


i = interest rate (the discount rate)


n = number of payment periods

Thanks for writing.

Staff
www.solving-math-problems.com

Oct 23, 2012
Thank you
by: Anonymous

I really love your website & always being so helpful to explain. Thank you so much

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