Question

You are trying to decide how much to save for retirement. Assume you plan to save $5,000 per year with the first investment made one year from now. You think you can earn 10% per year on your investments and you plan to retire in 43 years, immediately after making your last $5,000 investment. If, instead of investing $5,000 per year, you wanted to make one lump-sum investment today for your retirement that will result in the same retirement saving, how much would that lump sum need to be?

Answer 1

To decide how much to save for retirement. :-
For Regular Payment plan :-
plan to save $5,000 per year,
earn 10% per on my investments and
plan to retire in 43 years,
(The formula below assumes contributions occur at the end of each year.)

Balance = P(1 + r)Y   + c[ ((1 + r)Y - 1) / r ]
Where,
Y = No.of yrs for retirements plan,
P = Principal Investment,
c = Regular contribution,
r = rate of interest

=$5000(1 + 10%)43 + $5000[((1 + 10%)43 + 1 - 1 )) / 10% ]
=$5000(60.24) + $5000[((60.24) - (1.00)) / 0.10]
=$301,200 + $2,962,000
=$3,263,200 (Total Savings into 43 yrs including interest.)

Now we want to calculate lumpsum amt for one time payment and getting same maturity after 43 years.
We used Future Value formula for that,
FV = PV (1+i)^n
$3,263,200 = PV ( 1 + 10%)43
$3,263,200 = PV (1.10)43
Present Value = $3,263,200 / 60.24
= $54,169.98 or
= $54,170

Ans : One lump-sum investment today for my retirement that will result in the same retirement saving, i would save that lump sum need to be $54,170.