Introduction to Finance

Financial Calculator Solution:
Inputs: 5 
–1000 6153
N 
PMT 
FV
Press: DUE %i
Solution: 7.00
Spreadsheet Solution:
Excel’s RATE fi nancial function also can be used to solve for the interest rate involving an 
annuity due problem. The process is very similar to the one used for an ordinary annuity 
problem, except that a “1” value in “Type” is entered to indicate that cash fl ows occur at the 
beginning of each time period. The fi nancial function solution would be,
= RATE(Nper,Pmt,PV,FV,Type)
= 
RATE(5,–1000,0,6153,1)
= 
7.00%
The 
n
time periods involved in an annuity due problem also can be determined using 
either a computer software program or a fi nancial calculator. For example, in the preceding 
problem, let’s assume we know the interest rate is 7 percent, the future value is $6,153, and 
the payment is $1,000 (entered as –1000). What we don’t know is the number of time periods 
required. We can solve for N as follows:

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Questions and Problems
251
Financial Calculator Solution:
Inputs: 7 
–1000 6153
%i 
PMT 
FV
Press: DUE N
Solution: 5.00
Spreadsheet Solution:
Excel’s
 
NPER fi nancial function also can be used to solve for the number of periods in an 
annuity due problem. However, in contrast with an ordinary annuity, a value of “1” for “Type” 
must be entered to indicate that the cash fl ows occur at the beginning of the time periods. The 
fi nancial function solution would be the following:
= NPER(Rate,Pmt,PV,FV,Type)
= 
NPER(7,–1000,0,6153,1)
= 
5.00
Of course, the same process could be used for fi nding either interest rates or the number 
of time periods if the present value of the annuity due instead of the future value were known. 
This would be done by substituting the PV value for the FV value in fi nancial calculator or 
spreadsheet calculations.
Summary
LO 9.10 
An annuity due exists when equal periodic payments (or 
receipts) occur at the beginning of each time period. As was the case 
for ordinary annuities (where periodic payments occur at the end of 
each time period), necessary inputs include an interest rate, the number 
of periods, and a periodic payments variable. We then can solve for 
the future value (or present value) of the annuity due by modifying 
the solution methods used for ordinary annuities.
Questions and Problems
1. 
Assume you are planning to invest $100 each year for four years 
and will earn 10 percent per year. Determine the future value of this 
annuity due problem if your fi rst $100 is invested now.
2. 
Assume you are planning to invest $5,000 each year for six years 
and will earn 10 percent per year. Determine the future value of this 
annuity due problem if your fi rst $5,000 is invested now.
3. 
What is the present value of a fi ve-year lease arrangement with an 
interest rate of 9 percent that requires annual payments of $10,000 per 
year with the fi rst payment being due now?
4. 
Use a fi nancial calculator to solve for the interest rate involved 
in the following future value of an annuity due problem. The future 
value is $57,000, the annual payment is $7,500, and the time period 
is six years.