Steps for Solving A TVM Problem
1. Carefully read the entire problem, and
determine what you are being asked to find.
2. Write down all of the variables in the problem
and label them.
3. Does the interest rate’s compounding
frequency match the payment period?
4. Draw a Timeline.
5. Select the appropriate formula(s) and solve the
problem.
6. If the problem is complex, break it down into
smaller problems.
A Simple Example
(Chapter 5 Self-Test Problem 1) Assume
you deposit $10,000 today in an account
that pays 6 percent interest. How much
will you have in five years?
Self-Test Problem 5-1
1. After reading the problem, it is clear that you
are being asked to find a future value. (“…in
five years.”)
2. The following variables are given:
•
•
•
$10,000 – Present Value
6 percent compounded yearly – the interest rate
5 year – time over which the $10,000 will grow at
the 6 percent rate
3. Since this is a lump sum problem,
compounding frequency is not much of a
issue.
Self-Test Problem 5-1
4.
5. The appropriate formula is:
6. This is not a complex problem
A More Complex Example
(Chapter 6 Problem 52) A 5-year annuity of
ten $7,000 semiannual payments will
begin 8 years from now, with the first
payment coming 8.5 years from now. If the
discount rate is 10 percent compounded
monthly, what is the value of this annuity
five years from now? What is the value
three years from now? What is the current
value of the annuity?
Problem 6-52
1. This is a present value of an annuity
problem that is asking us to find the PV at
different points along the timeline.
2. N = 10; PMT = $7,000; Annuity is
deferred 8 years; 1st payment in 8.5
years; APR = 10% cpd monthly
3. No payments are made semiannually but
interest compounds monthly.
6
 0.10 
SA Rate = 1 
  1  5.105331332%
12 

Problem 6-52
Problem 6-2
5. Appropriate Formula:


1
1
  $53, 776.72243

PVA Year 8  $7000 
10
 0.0511... 0.0511... 1.0511... 
$53, 776.72243
 $39,888.33
PVYear 5 
6
1.0511...
PVYear 3 
$53, 776.72243
PVYear 0 
$53, 776.72243
1.0511...
10
1.0511...
16
 $32, 684.88
 $24, 243.67