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.

​$548 per month invested at 4​%, compounded​ monthly, for 5 ​years; then ​$717 per month invested at 6​%, compounded​ monthly, for 5 years.

Answer 1

Case 1

​$548 per month invested at 4​%, compounded​ monthly, for 5 ​years

PMT =548

r=4% =0.04

n=12

t=5

A=PMT[(1+r/n)^(nt) -1]/(r/n)

=548[(1+0.04/12)^(12*5) -1]/(0.04/12)

=548[0.220996]/0.00333

=548(66.2989)

=36331.84

Case 2

$717 per month invested at 6​%, compounded​ monthly, for 5 years.

PMT =717

r=6% =0.06

n=12

t=5

A=PMT[(1+r/n)^(nt) -1]/(r/n)

=717[(1+0.06/12)^(12*5) -1]/(0.06/12)

=717(0.34885/0.005)

=717*69.77

=50025.11

So final amount =36331.84 + 50025.11 =86356.95