MATH 104 Financial Math Formulas and Exercises
(I)
Retirement Plan
A = Goal Amount
a = Periodic Deposit Amount
n = # of periods
i = Periodic Interest Rate = (Annual Interest Rate)/(# of Periods/yr)
r=1+i
(1) To find A when a, n, i are known
ar(r n  1)
A
i
(2) To find a when A, i, n are known
a
Ai
r (r n  1)
(3) To find n when A, a, i are known
  Ai  
 ln 1  ar  
  , where [x] is the smallest integer larger than x
n 
 ln r



(II)
Present Value
P = the lump sum needed to be deposited to achieve the same goal A under the
same condition
a(r n  1)
P
n
ir
(III)
Loan Payment (Amortization)
(IV)
A = Loan Amount
1
(V)
(VI)
a = Periodic Payment
n = # of periods
i = Periodic Interest Rate = (Annual Interest Rate)/(# of Periods/yr)
r=1+i
(1) A 
a(r n  1)
rn i
(2) To find a when A, i, n are known
A rn i
a n
r 1
(3) To find n when A, a, i are known
a 

 ln a  iA 
n
 , where [x] is the smallest integer larger than x
 ln r 


2
Exercises
(I)
(1)Find the goal amount A when a, n, i are
a
n
200
240
250
300
275
320
400
450
350
420
i
0.0034
0.0040
0.0045
0.005
0.006
(2) Find the periodic deposit a when A, n, i are
A
400,000
450,000
475,000
600,000
550,000
n
440
500
420
450
460
i
0.0034
0.0040
0.0045
0.005
0.006
(3)Find the number of periods n needed to achieve A when A, a, i are
A
a
i
400,000
340
0.0034
450,000
300
0.0040
475,000
420
0.0045
600,000
450
0.005
550,000
460
0.006
(II)
Find the present value P when a, n, i are as in (I).
(1) Find periodic payment a when A, i, n are
A
400,000
450,000
475,000
600,000
550,000
n
440
500
420
450
460
i
0.0034
0.0040
0.0045
0.005
0.006
3
(2) Find the number of periods n needed to finish paying the load A when A, a, i are
A
a
i
400,000
340
0.0034
450,000
300
0.0040
475,000
420
0.0045
600,000
450
0.005
550,000
460
0.006
4