Question

You want to be a millionaire when you retire in 30 years and expect to earn 8.5 percent, compounded monthly. How much more will you have to save each month if you wait 10 years to start saving versus if you start saving at the end of this month?

Answer 1

Answer:

more will you have to save each month 981.9

Explanation:

given data

time = 30 year = 30 × 12 = 360 months

expected earn = 8.5 % = $\frac{0.085}{12}$ = 0.0070833

time = 10 year = 10 × 12 = 120 months

future value = millionaire = $10^{6}$  

solution

we consider here saving end of this month = x

and saving end of 10 year = y

now we solve for x

$10^{6}$ =  x × $\frac{1+ r^{t}}{r} - 1$    

$10^{6}$ =  x ×  $\frac{1+ 0.0070833^{360}}{0.0070833} - 1$    

x = 605.8

and

$10^{6}$ =  y × $\frac{1+ r^{t}}{r} - 1$

$10^{6}$ =  y ×  $\frac{1+ 0.0070833^{120}}{0.0070833} - 1$

y = 1594.9

so here we require more amount to save is y - x in end of each month = 1594.9  -  605.8  = 981.9

Answer 2

Answer:

558.11/month; 1301.78/month. You will have to save 743.67 more if you wait 10 years before saving.

Explanation:

In the annuity problem above, the future value is given as 1,000,000 and we need to estimate the amount to be saved today (C). Thus:

FVA = 1000000; C = unknown; r = 8.5%/12 = 0.7083%; t = 30*12 = 360.

$FVA = C[\frac{(1+r)^{t}}{r}]$

C = 1000000/1791.753 = 558.11/month

To wait for 10 years before saving means that t = 30-10 = 20 years = 20*12 = 240. Similarly,

FVA = 1000000; C = unknown; r = 8.5%/12 = 0.7083%; t = 20*12 = 240.

C = 1000000/768.18 = 1301.78/month

You will have to save(1301.78 - 558.11) 743.67 more if you wait 10 years before saving.