Question

You will get some practice calculating FV and FVA's that we learned about in this chapter for this DB, while also hopefully showing you something that could help you in your personal life!. Here try using the future value tables to show yourself the difference that waiting 10 years to start saving for retirement can make. Assume you are 27 and start saving $3,000/year. You do this for 10 years before circumstances prevent you from saving any more, but the money that has amassed will continue to sit and earn 10%, like it has from when you first started saving, until you retire at age 67 (another 30 years). So you will first use the FVA (Future Value of an Annuity) of $1 chart for $3,000 at 10% for 10 years; then use that resulting number in a FV of $1 chart for 30 years (periods) at 10% to see how much you would have at retirement. Next, assume you wait until age 37 to start saving, but no circumstances cause you to stop (A very rare occurrence in real life! Unexpected things almost always will happen to derail your best saving intentions!). SO for this one, you will use just the FVA chart, still using $3,000 and 10%. Show your work and results, as well as comments. Are you surprised by the results? I will comment on this later in the week after everyone has posted. Original posts should contain a minimum of 120 words.

Answer 1

first case: $834,290.82

second case: $493,482

Because the 10 years capitalized for more time the magic of compounding interest can do his work

Step-by-step explanation:

first case:

and annuity of 3,000 for 10 years

and then a lump sum for 30 years:

`C * ((1+r)^(time) -1)/(rate) = FV\\`

C 3,000

time 10 year

rate 10% = 0.1

`3000 * ((1+0.1)^(10) -1)/(0.1) = FV\\`

FV $47,812

`Principal \: (1+ r)^(time) = Amount`

Principal 47,812.00

time 30.00

rate 0.10000

`47812 \: (1+ 0.1)^(30) = Amount`

Amount 834,290.82

Second case:

annuity of 3,000 for 30 years:

`C * ((1+r)^(time) -1)/(rate) = FV\\`

C 3,000

time 30

rate 0.1

`3000 * ((1+0.1)^(30) -1)/(0.1) = FV\\`

FV $493,482