You are 35 years old today and are considering your retirement needs. You expect to retire at age 65 and your actuarial tables suggest that you will live until 100. Your living expenses in retirement will be $ 30,000 a year (starting at age 66 until 100).

a. How much will you need to have saved by your retirement date to afford that? Give formula.

b. Assume you already have $ 50,000 in retirement savings. If you can invest the money at 8% per year, how much would you need to save each year for the next 30 years to be able to afford this retirement plan?

c. What portion of your retirement wealth will you have saved by age 45 ? Give formula. 

 

QUESTION A

How much will you need to have saved by your retirement date to afford that? Give formula.

Funds required as on Retirement date (65th Birthday):

(i) Fund required on 65th birthday to make a move Bahamas = $300,000

(ii) Living expense of $30,000 a year starting end of year 66 to end of year 100

Interest rate = 8%

To calculate PV as on retirement date we will use PV function of excel

PV (rate, nper, pmt, fv, type)

= PV (8%, 35, -30000, 0, 0)

= $349,637.0465

Funds required as on Retirement date = $300,000 + $349,637.05 = $649,637.05

Funds required as on Retirement date = $649,637.05

Question B

How much would you need to save each year for the next 30 years to be able to afford this retirement plan

At age 35:

Savings = $50,000

Funds required on retirement date (65th birthday) = $649,637.05

To get required yearly saving we will use PMT function of excel:

PMT (rate, nper, pv, fv, type)

PMT (8%, 30, 50000, -649637.05, 0)

=$1,293.26

Annual saving required = $1,293.26

Question C

What portion of your retirement wealth will you have saved by age 45 ? Give formula. 

FV = PV (1 + Interest rate)^ ^{Number of years}

Future value of 50,000 savings = $50,000 * (1 + 8%)^ ³⁰ = $503,132.844 =$503,132.84

Balance fund required as of retirement date from annual savings = $649,637.0465 - $503,132.844 = $1,46,504.20

Annual savings required after 5 years:

= PMT (8%, 25, 0, -146504.20, 0)

= $2004

Annual savings required after 5 years = $2004