Kenneth R. Szulczyk
ܸܲ=(ଵା.)బ+(ଵା.)భ+(ଵା.)మ+(ଵା.)య=$1, 836. 51 ( 9 )
If you received $1,836.51 as a lump sum today, you could invest this money into a savings
account and earn $2,187.31 in three years at 6% interest. We converted a multiple stream
investment into a single deposit investment.
Present value formula is flexible because it can handle uneven withdrawals and
investments. For example, you do the following activities with your bank account in Table 8.
Table 8. Withdrawals and Deposits for a Bank Account
Year Activity Amount Interest + Balance
0 Deposit $100 $148.15
1 Deposit $300 $389.88
2 Withdrawal $50 - $57
2 Deposit $100 $114.00
3 Withdrawal $75 - $75
Total $520.03
Withdrawal or deposit determines the sign. A withdrawal is negative, while a deposit is
positive. Furthermore, the interest plus balance column in Table 8 includes the interest rate that
the deposit would earn if held it until the end of the third year. For example, you deposited $100
into your account at Time 0 that grew into $148.15 in 3 years at 14% interest. Moreover, you
withdrew $50 in Time 2, which would earn $57 for the next two years. However, you withdrew
it, making it negative. Value of your withdrawals and deposits equals $520.03 at the end of Year
3.
We use the present value formula to calculate today’s value of these cash flows. You would
be indifferent about receiving a lump-sum payment of $351.01 today or $52 0 .03 in three years.
We calculated the present value in Equation 10.
ܸܲ=(ଵା.ଵସ)బ+(ଵା.ଵସ)భ+
ି
(ଵା.ଵସ)మ+
ି
(ଵା.ଵସ)య=$351.^01 (^10 )^
If you invested $351.01 today at 14% interest, then in 3 years, you would have $520.04, the
final balance of your bank account.
Compounding Frequency
Financial analysts always define an interest rate as an annual term, called the Annual
Percentage Rate (APR). The APR come from the Federal Reserve’s regulation that helps
prevent fraud. For example, do you consider a 1% interest rate a good interest rate to charge a
borrower? Unfortunately, we do not know the time period this interest rate applies to because
the time period was omitted. If the 1% is annual, then it is an excellent interest rate for a loan.