Question

You are considering two different strategies for a savings account that you intend to close when you retire exactly 29 years from today. For Strategy 1, deposit $1,750 per quarter for 8 years (first deposit today; last one exactly 8 years from today); no new deposits will be made after the end of the deposit period, but interest continues to accrue until the account is closed. For Strategy 2, you’ll make your first quarterly deposit exactly 8 years from today, each quarterlydeposit also equals $1,750 , and you’ll continue making quarterly deposits for 21 years, so that you make the final deposit exactly 29 years from today when you close the account. The savings rate always is 10.5% compounded quarterly.

What will strategy 1 accumulate at retirement?

Answer 1

First thing to notice here is that the total quarters in 29 years=4*29=116

Secondly, the deposits are made at the begining of the quarter and for the first 33 payments you made $1750 per quarter. ((8*4)+1=32+1=33)

Use FV function in EXCEL.

=FV(rate,nper,pmt,pv,type)

rate=10.5%/4=2.625%

nper=number of quarters=33

pmt=1750

pv=0

type=1, because the payments are made at the begining of the quarter

=FV(2.625%,33,-1750,0,1)

FV=$92,468.69

This amount will again increase by the quarterly compunding rate for next 83 quarters (116-33=83)

Future value=Present value*(1+r)^n

=92468.69*((1+2.625%)^83)

=92468.69*8.59039

=$794,342.57

The total accumulated value after 29 years=$794,342.57