Question

In: Finance

You would like to start saving for your retirement and are trying to figure out how...

  1. You would like to start saving for your retirement and are trying to figure out how much to save.   You estimate that you will need $350,000 per year for the 30 years you’ll be retired. In addition, you’d like to have an additional $85,000 in your fifth year of retirement to buy a boat (This money should be in addition to the $300k you are withdrawing). Assume that you plan to save an equal amount of money every year, starting next year for the 35 years you will be working (save in years 1-35, withdraw in years 36 -65, buy boat in year 41). Assume that you will earn 8% on your portfolio during the years you save, but only 5% for the years you are retired. How much do you need to save each year in equal amounts to meet this goal?

Solutions

Expert Solution

You are planning to make a total of 30 annual withdrawals of $350,000 after retirement. After retirement you will be able to earn 5 percent per year

Therefore Present value of the total of 30 annual withdrawals of $350,000 at the time of retirement can be calculated with the help of PV of an Annuity formula

PV1 = PMT * [1-(1+i) ^-n)]/i

Where,

Present value at the time of retirement (PV) =?

PMT = Annual payment = $350,000

n = N = number of payments = 30 years

i = I/Y = interest rate per year =5%

Therefore,

PV1 = $350,000* [1- (1+5%) ^-30]/5%

= $5,380,357.86

In addition, you’d like to have an additional $85,000 in your fifth year of retirement to buy a boat

Therefore PV of this amount at the time of retirement

PV2 = FV/ (1+i) ^n

Where,

Present Value PV =?

Future value FV=$85,000

Annual interest rate i = 5%

Time period n = 5 years

Therefore,

PV2 = $85,000/ (1+5%) ^5

= $66,599.72

Total amount required at the time of retirement = PV1 + PV2 = $5,380,357.86 + $66,599.72

= $5,446,957.58 (Now this amount will be future value of all savings)

Your retirement account will have $5,446,957.58

We can use FV of an Annuity formula to calculate the annual savings by you

FV = PMT *{(1+i) ^n−1} / i

Where,

Future value of annual savings FV = $5,446,957.58

PMT = Annual savings =?

n = N = number of payments = 35 years

i = I/Y = interest rate per year =8%

Therefore,

$5,446,957.58 = Annual savings *{(1+8%) ^35−1} /8%

Annual savings = $31,610.14

Therefore you have to save $31,610.14 per year to achieve your retirement goal.


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