The second question, how much interest I earned, can be answered by subtracting the total
payments from the future value. I made 15 payments of $2,500 each, and 5 payments of
$1,000 each, so the total payments were 15($2,500) 5($1,000) $42,500. So the total
interest earned was $99,549.11 $42,500 $57,049.11.“Sinking Funds” That Don’t Start from Scratch
Sometimes we have a set goal for a sinking fund, but already have some funds in the account
working toward our goal. The following example will illustrate how we can address this
sort of situation.Example 4.7.5 Alexis will be retiring in 5 years, and wants to have a balance of
$600,000 in an investment account at that time. Right now, she has $375,000 in this
account. She expects her account to earn 8.4%. How much does she need to deposit
each month to reach this goal?Since Alexis already has quite a bit of money in her account, her payments only need to
make up the difference between what she will already have and the $600,000 target. The
money she has, though, will keep earning interest for these next 5 years, and so we need to
see how much it will grow to.Bucket 1: The $375,000 with its interest.FV PV(1 i)n
FV $375,000(1.007)^60
FV $569,901.11Since she can expect this much in her account without making payments, the payments just
need to make up the difference. So their future value must be $600,000 $569,901.11
$30,098.89.Bucket 2: A sinking fund with a $30,098.89 future value.FV PMT s _n (^) | (^) i
$30,098.89 PMT s __ 60 | (^) .007
PMT $405.38
So monthly payments of $405.38 would be enough to fi ll the gap.
Dealing with problems like the ones in this section can be a challenge. Take your time
and think each one through; these are not the sort of problems that you can expect to coast
through on autopilot. Keep in mind that, when you break a problem up into buckets, every
dollar and its interest must be included in one, but only one, of the buckets. Also, don’t be
afraid to look back at the examples; while not every problem will match up with one of
them, the ideas exploited in the examples can be put to use in other situations as well.
EXERCISES 4.7
A. “Annuities” That Don’t Start from Scratch
- HuperMart Convenience Stores Corp. has $1,598,375 in an account set aside for longer term employee benefi t
commitments. The company is depositing $37,500 each quarter into this account. Assuming these deposits continue,
and assuming the account earns 7½%, how much will it have in this account in 10 years? - Trevor has $296,101.43 in his 401(k). Assuming he keeps up deposits of $275 each month and his account continues
Copyright © 2008, The McGraw-Hill Companies, Inc.to earn 7.825%, how much will he have in his 401(k) when he retires in 20 years?
Exercises 4.7 199