Question

Calculate the future value of an account after​ you've contributed ​$1 comma 050 at the end of each year for 40 years assuming you can earn 6.00 percent compounded​ annually, and that you​ don't make a withdrawal during the​ 40-year period. Now calculate the value of the same account if you stop making contributions after 30 years. What does this tell you about the power of time when trying to accumulate​ wealth?

Answer 1

Case 1. $354,776

Case 2. $143,122

This shows that investment would loose its value by $211,654.

Step-by-step explanation:

As we know that:

Future Value = PMT / Annuity Factor (Step 1)

The periodic payments are represented as PMT which is $1,050.

Step 1:

And as we know:

Annuity Factor = ((1 + r)^n - 1 ) / r

Here,

r is the rate of return which is 9%.

Case 1: So for n=30 years:

Annuity Factor = ((1+ 9%)^30 years - 1) / 9% = 136.307

By putting value in the first equation, we have:

FV at 40 years of consistent periodic payments = $1050 * 337.882

= $354,776

Case 2: So for n=40 years:

Annuity Factor = ((1+ 9%)^40 years - 1) / 9% = 337.882

By putting value in the first equation, we have:

FV at 30 years of consistent periodic payments = $1050 * 136.307

= $143,122

The difference between the two scenarios is $211,654, which means the invesmtnet will loose its value by this amount.