Question

Find the final amount in the following retirement​ account, in which the rate of return on the account and the regular contribution change over time. ​$322 per month invested at ​4%, compounded​ monthly, for ​5 years; then 440​$ per month invested at ​5%, compounded​ monthly, for 5 years.

Answer 1

Total value of the investment= $57,320.73

Step-by-step explanation:

First, we need to calculate the future value of the first part of the investment. We will calculate the future value for the monthly deposit for five years and then the lump sum for another five years.

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

A= monthly deposit

i= 0.04/12= 0.003333

n= 5*12= 60 months

FV= {322*[(1.003333^60) - 1]} / 0.003333

FV= $21,348.05

For the lump sum:

FV= PV*(1+i)^n

n= 12*5= 60

i= 0.05/12= 0.004167

FV= 21,348.05*(1.004167^60)

FV= $27,397.75

Now, the future value of the second part of the investment:

n= 60

i= 0.0041667

A= 440

FV= {440*[(1.004167^60) - 1]} / 0.004167

FV= $29,922.98

Total value of the investment= 27,397.75 + 29,922.98

Total value of the investment= $57,320.73