Basic Formulas of Finance
Main Idea: A certain amount of money is deposited (or borrowed). This amount of money earns (or accrues) interest.
Terminology:
P = principal – the amount deposited (or borrowed)
r = annual rate of interest
t = time (IN YEARS) that the principal earns (or accrues)
I = total amount of interest earned (or accrued)
A = P + I – accumulated amount (principal & interest combined)
The formula for simple interest is: I = Prt and A = P + I.
Example: Janice purchases a bond for $1000.00 that pays 3.5% simple interest.
(a)
If the bond is held for 2 years, how much interest is earned?
I = Prt = 1000(.035)(2) = $70.00
(b)
What would be the total value of the bond?
A = P + I = 1000.00 + 70.00 = $1070.00
(c)
If the bond is held for 30 months, how much interest is earned?
I = Prt = 1000(.035)(30/12) = 1000(.035)(5/2) = 1000(.035)(2.5) = $87.50
(Remember that the time has to be expressed in YEARS not months)
Although simple interest is indeed simple, in reality, simple interest is not widely used. Most of the time, the
interest itself is added back to the principal so that it too earns interest. This process is called compounding and
interest that itself earns interest is called compound interest.
For compound interest then, we must know how often the interest is added back to the principal in order to
calculate the amount of interest accrued. The standard way to do this is to specify the number of compounding per
year. We will use the letter m to stand for this quantity.
m (the # of compounding periods/year)
1
2
4
12
in words
annually
semi-annually
quarterly
monthly
Once we know m, we can easily figure out how many compounding periods there are for the entire time (t) that the
money earns interest. For example, if interest is compounded quarterly (m=4) for t=2 years, then there are 4(2) = 8
compounding periods. In other words, the total # of compounding periods, n is calculated as n = mt.
We also have to consider that once we break a year down into m compounding periods, we also have to determine
the interest rate per compounding period. We will call this quantity (interest rate/period) i. That means that i is
calculated as i = r/m.
For example, if we continue with the previous example (with m = 4) and use an annual interest rate (r) of 4%, then a
4% annual interest rate divided up over 4 compounding periods per year would yield an interest rate of 4%/4 = 1%
per period.
Putting all of this together, the standard formula for compound interest problems is:
Notice that this formula is written to give A (the accumulated amount after t years) instead of I (the total amount of
interest). If you do want I, just remember that I = A – P. (I is the difference between the accumulated amount and
the principal.)
Example: Oscar deposited $2000 in an account paying 3.2% compounded semi-annually.
(a)
How much will be in the account after 3 years?
A = 2000(1 + .032/2)2(3) = 2000(1 + 0.016)6 = 2000(1.016)6 = 2000(1.099922909) = $2199.85
(b)
How much interest was earned over the 3 year period?
I = A = P = $2199.5 - $2000.00 = $199.85
NOTE: In order to successfully do problems of this type, you MUST learn how to use certain functions on the calculator. In
this course, you are only allowed to use the CASIO fx-260 SCHOOL edition calculator.
So,
1.
2.
3.
You have to practice on the CASIO fx-260 SCHOOL edition calculator.
The button used to raise a number to a power is xy.
Do NOT round off too much during intermediate calculations. Often, you will give your final answer to the
nearest cent BUT if you round off too much on intermediate steps, your final answer may not be accurate to the
nearest cent.
Example: Alice invested a certain amount in an account paying 2.8% interest compounded monthly. If at the end of 4 years,
she had $6240.00 in the account, how much did she start off with?
6240 = P(1 + .028/12)12(4)
6240 = P(1.00233333)48
6240 = P(1 + 0.00233333)48
6240 = P(1.118366944767)
P = 6240 / 1.118366944767)
P = $5579.56