Time Value of Money
~Simple Interest and Compound Interest~
Hakimul Batih
C11050314 Ekonomi Teknik
S1 Teknik Elektro
Institut Teknologi PLN (IT PLN)
Newman, D.G., et.al. Engineering Economic Analysis, Oxford University Press.
Would you rather: (1) receive $100 today or (2) receive $100 next
year?
Time value of money
• We often find that the monetary consequences of any alternative occur
over a substantial period of time-say, a year or more.
• When monetary consequences occur in a short period of time, we simply
add up the various sums of money and obtain a net result.
• But can we treat money this way when the time span is greater?
• Money is quite a valuable asset-so valuable that people are willing to pay
to have money available for their use.
• Money can be rented in roughly the same way one rents an apartment,
only with money, the charge is called interest instead of rent.
• The importance of interest is demonstrated by banks and savings
institutions continuously offering to pay for the use of people's money to
pay interest
Time value of money
• If the current interest rate is 9% per year, and you put $100 in to the bank
for one year, how much will you receive back at the end of the year?
• You will receive your original $100 together with $9 interest, for a total of
$109
• This example demonstrates the time preference for money, we would
rather have $100 today than the assured promise of $100 one year hence;
but we might well consider leaving the$100 in a bank if we knew it would
be worth $109 one year hence.
• This is because there is a time value of money in the form of the
willingness of banks, businesses, and people to pay interest for the use of
various sums.
Simple Interest
• Simple interest is interest that is computed only on the original sum and
not on accrued interest.
• Thus if you were to loan apresent sum of money P to some one at a simple
annual interestrate i (stated as a decimal) for aperiod of n years,the
amount of interest you would receive from the loan would be:
Total interest earned = P x i x n = Pin
• At the end of n years the amount of money due you, F, would equal the
amount of the loan P plus the total interest earned. That is, the amount of
money due at the end of the loan would be:
F = P + Pin = P(1+in)
• In Example 3-3 the interest earned at the end of the first year is
(5000)(0.08)(1)= $400, but this money is not paid to the lender until the end
of the fifth year.
• As a result, the borrower has the use of the $400 for 4 years without paying
any interest on it.
Compound Interest
• In practice, interest is computed using the compound interest
method.
• For a loan, any interest owed but not paid at the end of the year is
added to the balance due. Thus, the next year's interest is calculated
based on the unpaid balance due ,which includes the un paid interest
from the preceding period. In this way, compound interest can be
thought of as interest on top of interest. This distinguishes compound
interest from simple interest.
Compound Interest
𝑭𝒖𝒕𝒖𝒓𝒆 𝒔𝒖𝒎 = 𝑷𝒓𝒆𝒔𝒆𝒏𝒕 𝒔𝒖𝒎 ∙ (𝟏 + 𝒊)𝒏
𝑭 = 𝑷 ∙ (𝟏 + 𝒊)𝒏
i = interest rate per interest period. In the equations the interest rate is stated as a decimal (that is,9% interest is
0.09)
n = number of interest periods.
P =a present sum of money.
F = a future sum of money.
The future sum F is an amount, n interest periods from the present, that is equivalentto P with interest rate i.
Single Payment Coumpond Interest
• Single payment compound amount formula and is written in
functional notation as
F = P (F/P, i, n)
• The notation in parentheses (F /P, i, n) can be read as follows:
“To find a future sum F, given a present sum, P, at an interest rate i
per interest period, and n interest periods”