Question

Over the next 20 years, you deposit money into a retirement account at the end of each year according to the following schedule: Time Amount invested each year 1 - 5 $2000 6 - 10 $3000 11 - 20 $5000 The effective annual rate of interest is 9%. Find the accumulated value of your account at time 20.

Answer 1

Answer:

Total FV= $162,067

Explanation:

First, we will calculate the ending value of each investment of an equal amount. Then, the total future value.

For annual deposits:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

For total capital:

FV= PV*(1+i)^n

First part:

FV= {2,000*[(1.09^5) - 1]} / 0.09

FV= $11,969.42

FV= 11,969.42*1.09^15= $43,598.40

Second part:

FV= {3,000*[(1.09^5) - 1]} / 0.09

FV= $17,954.13

FV= 17,954.13*1.09^10= $42,503.95

Third part:

FV= {5,000*[(1.09^10) - 1]} / 0.09

FV= $75,964.65

Finally, the total future value:

Total FV= 43,598.40 + 42,503.95 + 75,964.65

Total FV= $162,067