Question

You have a couple who are 31 years old, and want to retire at the age of 67. Knowing that, the couple has a combined annual income of $95,000 today.

1. If the couple want to procrastinate their retirement savings until they reach 35, and if retirement savings will grow at a rate of 8%, how much would they need to save per year, at the end of every year, in order to achieve the $2 million target by the time they retire? They will have no savings for this purpose as they begin their retirement program.

2. Assume they have $15,000 already set aside for the purpose of retirement, how much would they have to save every year, at the beginning of each year starting now, in order to attain the goal of $2 million by the time they retire? Assume they are able to achieve an average rate of return on their savings of 8%.

3. If they have retired with $2 million in savings, and they want to withdraw $120,000 every year for living expenses at the beginning of each year, how long can their retirement nest egg last (in years) if the rate of return on their savings is 5% post-retirement?

Please also show formulas for each.

Answer 1

1. FV at age 67 =2000000
Rate =8%
Number of years =32
The Savings per year =FV/((1+r)^n-1)/r) =2000000/(((1+8%)^32-1)/8%)=14901.63

2. Amount today =15000
FV =PV*(1+r)^n+(1+r)*PMT*(((1+r)^n-1)/r)
2000000=15000*(1+8%)^36+(1+8%)*PMT*(((1+8%)^36-1)/8%)
2000000-239522.5776=PMT*202.07032
PMT or annual savings =8712.20

3.Rate =5%
Retirement fund (PV)=2000000
PMT =120000
Number of Years retirement next egg can last using formula
PV =(1+r) *PMT*(((1-(1+r)^-n)/r)
2000000=120000*(1+5%)/5%*((1-(1+5%)^-n)
0.793650793650794 =1-1.05^-n
1.05^-n =1-0.793650793650794
for number of periods
n =-log(0.793650793650794 )/log(1.05) =4.74 years

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