Question

Assume that you can invest money in a savings account with an APR of 8.0% and semi-annual compounding.

1. A perpetuity will pay $500 every 6 months. However, the payments don't begin for 30 months. What is the present value of this perpetuity?

2. What is the pv of a perpetuity that pays $500 every 18 months and that makes its first payment in 18 months?

Answer 1

1.

=500/1.04^5+500/1.04^6.....

=500/1.04^5*1/(1-1/1.04)

=10685.05

2.

=500/1.04^3+500/1.04^6...

=500/1.04^3*1/(1-1/1.04^3)

=500/(1.04^3-1)

=4004.36