Question

1. You have just turned 22, and you intend to start saving for your retirement. You plan to retire in 43 years when you turn 65. During your retirement, you would like to have an annual income of$120,000 per year for 26years (until age 91).

a)Calculate how much you need to have in your account before the first withdrawal at age 66.

b)Calculate how much you would have to save annually between now and age 65 in order to finance your retirement income and to fill that account.

Make the following assumptions:

Assume that the relevant compounded interest rate is 4 percent per year.

You make the first deposit today and the last deposition the day you turn 65 (44 deposits in total).

You make the first withdrawal when you turn 66and the last withdrawal when you turn 91(26 withdrawals).

(PLEASE SHOW STEP-BY-STEP EXCEL FORMULA WITH FUNCTIONS)

Answer 1

A: Amount required before the first withdrawal

Using financial calculator

Input: N =26

I/Y = 4

PMT = -120000

Solve for PV as 1,917,932.30

Hence amount required before first withdrawal = $1,917,932.30

B: Since the deposits are made at the beginning of periods, this is annuity due.

n=44

Rate = 4%

Fv of annuity due= 1,917,932.30

Future Value of annuity due= (1+Rate)*A*((1+rate)^number of periods-1)/rate

1,917,932.30 = 1.04*A*(1.04^44-1)/0.04

1,917,932.30=120.029392 *A

A = 1,917,932.30/ 120.029392

= 15978.86

Amount to be saved annually =15978.86

Excel formula