# 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?

### Comments for Early Retirement – Lump Sum vs. Payments

 Oct 01, 2012 Lump Sum vs. Payments by: Staff Answer: Part I Present value of stream of future payments.       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 --------------------------------------------------

 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 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)nA = 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 = PVPV = A*(1 + i)-nSince 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 periodsThanks 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