(Question 1). Assume a 6% interest rate and annual compounding in the following

Question

(Question 1). Assume a 6% interest rate and annual compounding in the following two scenarios: (1) Assume Ace put aside $100,000 a year for 4 years, making payments at the end of each of those four years. Ace then just let the money accumulate interest for 6 more years. How much money would Ace have after the 10-year period? (2) What would the amount be in 10 years if Ace saved for the first 4 years by making payments at the beginning of each of those four years (assuming everything else is the same as scenario (1) above)?

(Qustion 2) Assume an 8% interest rate and annual compounding in the following two scenarios: (1) Assume Ace will not retire for 5 years. Beginning with the end of year 6, he will make the first of ten annual withdrawals of $100,000 from his retirement account (i.e., through year 15). What must Ace have in his retirement account today in order to make those annual withdrawals? (2) What must Ace have in his retirement account today if he makes the first of the ten annual withdrawals at the beginning of year 6 (assuming everything else is the same as scenario (1) above)?

Explanation / Answer

QUESTION - 1

(1)

Future value (FV) of the annual saving ($) = 100,000 x FVIFA(6%, 4) = 100,000 x 4.3746 [From FVIFA table]

= 437,460

FV of this amount, compounded for next 6 years ($) = 437,460 x (1.06)6 = 437,460 x 1.4185

= 620,537

(2) This is called an annuity due. In this case,

Future value (FV) of the annual saving ($) = 100,000 x FVIFA(6%, 4) x (1.06)

= 100,000 x 4.3746 x 1.06 = 463,708

FV of this amount, compounded for next 6 years ($) = 463,708 x (1.06)6 = 463,708 x 1.4185

= 657,769

NOTE: First question is answered.

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