In: Finance
Decision #2: Planning for Retirement
Erich and Mallory are 22, newly married, and ready to embark on the journey of life. They both plan to retire 45 years from today. Because their budget seems tight right now, they had been thinking that they would wait at least 10 years and then start investing $3000 per year to prepare for retirement. Mallory just told Erich, though, that she had heard that they would actually have more money the day they retire if they put $3000 per year away for the next 10 years - and then simply let that money sit for the next 35 years without any additional payments – then they would have MORE when they retired than if they waited 10 years to start investing for retirement and then made yearly payments for 35 years (as they originally planned to do). Please help Erich and Mallory make an informed decision:
Assume that all payments are made at the END a year (or month), and that the rate of return on all yearly investments will be 7.2% annually.
(Please do NOT ROUND when entering “Rates” for any of the questions below)
b2) How much will the amount you just computed grow to if it remains invested for the remaining 35 years, but without any additional yearly deposits being made?
a) | Future value of annuity | = | P[{(1+r)^n}-1]/r | ||||||
where | |||||||||
P | = | 3000 | |||||||
r | = | 7.2% or 0.072 | |||||||
n | = | 45-10 = 35 years | |||||||
Money after 45 years | = | 3000*[{(1+0.072)^35}-1]/0.072 | |||||||
= | 3000*[11.3977-1]/0.072 | ||||||||
= | 3000*10.3977/0.072 | ||||||||
= | $ 433,237.50 | ||||||||
b) | Future value of annuity | = | P[{(1+r)^n}-1]/r | ||||||
where | |||||||||
P | = | 3000 | |||||||
r | = | 7.2% or 0.072 | |||||||
n | = | 10 years | |||||||
Money after 10 years | = | 3000*[{(1+0.072)^10}-1]/0.072 | |||||||
= | 3000*[2.004-1]/0.072 | ||||||||
= | 3000*1.004/0.072 | ||||||||
= | $ 41,833.33 | ||||||||
b2) | Future value | = | Amount*(1+r)^n | ||||||
where | |||||||||
amount | = | $41,833.33 | |||||||
n | = | 35 years | |||||||
r | = | 0.072 | |||||||
Future value | = | 41833.33*(1+0.072)^35 | |||||||
= | 41833.33*11.3977 | ||||||||
= | $ 476,803.75 | ||||||||
c) | Future value of annuity | = | P[{(1+r)^n}-1]/r | ||||||
where | |||||||||
P | = | 3000 | |||||||
r | = | 7.2% or 0.072 | |||||||
n | = | 45 years | |||||||
Money after 45 years | = | 3000*[{(1+0.072)^45}-1]/0.072 | |||||||
= | 3000*[22.8436-1]/0.072 | ||||||||
= | 3000*21.8436/0.072 | ||||||||
= | $910,150 | ||||||||
d) | Future value of annuity | = | P[{(1+r)^n}-1]/r | ||||||
where | |||||||||
P | = | 250 | |||||||
r | = | 7.2% /12 =0.6% or 0.006 | |||||||
n | = | 45 years*12 months=540 | |||||||
Money after 45 years | = | 250*[{(1+0.006)^540}-1]/0.072 | |||||||
= | 250*[25.2877-1]/0.006 | ||||||||
= | 250*24.2877/0.006 | ||||||||
= | $ 1,011,987.50 | ||||||||
e) | Future value of annuity | = | P[{(1+r)^n}-1]/r | ||||||
where | |||||||||
P | = | ? | |||||||
r | = | 7.2% or 0.072 | |||||||
n | = | 20 years | |||||||
$1,000,000 | = | P*[{(1+0.072)^20}-1]/0.072 | |||||||
$1,000,000 | = | P*[4.0169-1]/0.072 | |||||||
$1,000,000 | = | P*3.0169/0.072 | |||||||
$1,000,000 | = | =P*41.902 | |||||||
1000000/41.902 | = | P | |||||||
$23,865 | = | P | |||||||
They need to put $ 23,865 for 20 years to accumulate $1,000,000 at their retirement. | |||||||||
Note- | In requirement (d) the monthly rate can also be taken as [(1.072)^1/12]-1 = 0.005811 or 0.5811% considering 7.2% as effective annual rate | ||||||||
There may be slight difference in answer due to decimal places.Please do not downvote on that basis | |||||||||
Please upvote the answer | |||||||||
If you have doubt,feel free to ask in comments |