You are currently 30 years old. You intend to retire at age 60, and you want to

Question

You are currently 30 years old. You intend to retire at age 60, and you want to be able to receive a 20-year, $100,000 beginning-of-the-year annuity, with the first payment to be received on your 60th birthday. You would like to save enough money over the next 15 years to achieve your objective; that is, you want to accumulate the necessary funds by your 45th birthday. A. If you expect your investments to earn 12% per year over the next 15 years and 10% per year thereafter, how much must you accumulate by the time you reach age 45? B. What equal, annual amount must you save at the end of each of the next 15 years to achieve your objective, assuming you currently have $10,000 available to meet your goal? Assume the conditions stated in section A. How do I do this with a financial calculator?

Explanation / Answer

first calculate the amount required at the 60 years of age. Use the following inputs in financial calculator

FV = 0

N = 20

PMT = 100,000

1/Y = 10%

use PV function in financial calculator (set the mode to BGN)

value at 60 years = 936,492.01

value at 45 years = 936,492.01/1.1015 = 224,188.74

now use the following input in the financial calculator

FV = 224,188.74

PV = 0

1/Y= 12%

N = 15

use PMT function in business calculator and set the mode to END

A. equal annual amount = 32,916.34

B.

use the following input in the financial calculator

FV = 224,188.74

PV = -10,000

1/Y= 12%

N = 15

use PMT function in business calculator and set the mode to END

B. equal annual amount = 32,648.10

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