Inputs: PMT = $1,000

N = 5

I/YR = 15%

PV: Use function wizard (PV) PV = $3,352.16

FV: Use function wizard (FV) FV = $6,742.38

g. How would the PV and FV of the above annuity change if it were an annuity due rather than an ordinary annuity?

For the PV, each payment would be received one period sooner, hence would be discounted back one less year. This would make the PV larger. We can find the PV of the annuity due by finding the PV of an ordinary annuity and then multiplying it by (1 + I).

PV annuity due = x =

Exactly the same adjustment is made to find the FV of the annuity due.

FV annuity due = x =

h. Excel does not have a function for the sum of the future values for a set of uneven payments. Therefore, we must find this FV by some other method. Probably the easiest procedure is to simply compound each payment, then sum them, as is done below. Note that since the payments are received at the end of each year, the first payment is compounded for 2 years, the second for 1 year, and the third for 0 years.

Year Payment x (1 + I )^(N-t) = FV

1 100 1.17 116.64

2 200 1.08 216.00

3 400 1.00 400.00

Sum = $732.64

An alternative procedure for finding the FV would be to find the PV of the series using the NPV function, then compound that amount, as is done below:

PV =

FV of PV =