FM Lial 9th
Financial Formulas Sp10
Using Financial Formulas
Definitions of Variables
Variable
Name
Meaning / Comments
I
Interest
P or PV
Principal or Present Value
r
Rate or Annual Interest Rate
Interest rate for one year. It is usually given as a percentage. Decimal form is used
in formulas. To convert between percentage and decimal form, move the decimal
two places to the left. Examples: 4% = .04; 5.6% = .056; 3.75% = .0375
t
Time
Time must be in years. 1 year = 12 months = 52 weeks = 365 days (exact interest)
or 360 days (ordinary interest)
A or S or FV
Accumulated Value or Future Value or Sum
R
Payment
m
Number of Compoundings per Year
n
Total Number of Compoundings
i
Periodic Interest Rate
income earned from loaning money or fee paid to borrow money
a lump sum of money being borrowed or loaned
The accumulated or future value is the sum of the principal and the interest.
Payments are periodic deposits, whereas principal is a single lump sum borrowed or
loaned.
annually: m = 1; semi-annually: m = 2; quarterly: m = 4; monthly: m = 12;
weekly: m = 52; daily: m = 365 (exact interest) or m = 360 (ordinary interest)
n = m∙t; total number of compoundings for the entire term of the investment or loan
i
r
m
; interest rate per period (i.e., per quarter, per month, per week, etc.)
1
FM Lial 9th
Financial Formulas Sp10
Formulas
Formula
When to Use
I = Prt
Use to find the simple interest earned on an investment or paid on a loan.
Loans with terms of one year or less usually charge simple interest. Simple interest is
charged or earned only on the principal and not on past interest. If you know any
three of the variables in the formula, you can solve for the fourth.
A = P(1 + rt)
Use to find the accumulated / future value of a simple interest loan or investment.
P
A
1  rt
Use to find the principal / present value of a simple interest loan or investment.
I=A–P
r 

A  P1 
m


mt 
Use to find the total interest earned on an investment or paid on a loan
Use to find the accumulated / future value of an account earning compound
interest. The principal is a single lump sum. No periodic payments are made.
 P(1  i)n
Hints
To solve for r in the compound interest formula:
1) Divide both sides by P. 2) Take the nth (n = m∙t) root of both sides. 3) Subtract one from both sides. 4) Multiply both sides by m.
To solve for t in the compound interest formula:
1) Divide both sides by P. 2) Take the natural log (ln) of both sides. 3) Rewrite the right side by bringing the exponent down in front of the logarithm.
4) Isolate t by dividing both sides by m  ln 1 mr .

P
r 

 A 1 
mt 

 m
r 

1  
 m
A
mt 
r 

re   1  
m



m
1

A
1 in
 A 1 in
Use to find the principal / present value of an account earning compound interest.
The principal is a single lump sum. No periodic payments are involved.
Use to find the effective rate / annual percentage rate (APR) for a given nominal /
stated rate. An effective rate is a simple interest rate that will yield the same result as
the stated compound interest rate.
2
FM Lial 9th
Financial Formulas Sp10
Formula
When to Use
mt   

  1 r 
 1 

 m 
 1 in  1 


S  R
 R



i
r 






m







RS
r 
 
m
mt  

 1  r 
 1
 m 



S

Use to find the future value of an ordinary annuity. With an ordinary annuity,
payments are made at the end of each time period.
Use to find the payment for the future value of an ordinary annuity. This is also
known as a sinking fund payment. A sinking fund is an account set up to receive
periodic deposits in order to accumulate a specified amount of money in a specified
amount of time.
i
1 i  1
n
mt 1  

  1 r 
 1 

 m 
 1 in1  1 


S  R
 R  R
 R


i
r 


 


m
 






mt   


 1 1 r 

  m 
 1 1 in


P  R
 R
i


r 

 


m





R P
r 
 
m



i
 P

n
mt  
 
 1 1 i 
1 1 r 

  m






Use to find the future value of an annuity due. With an annuity due, payments are
made at the beginning of each time period.
Use to find the present value of an ordinary annuity. The present value of an
annuity is the single lump sum that would produce the same final balance as the
annuity.
Use this to find the payment for the present value of an ordinary annuity. This is
also the formula for finding the payment for an amortized loan. A loan is amortized if
both the principal and the interest are paid by a sequence of equal periodic payments.
3