Present Value of an Annuity

Consider the following scenarios for an annuity with a $1000 payment amount C:

a. If you invest the $1,000 at the end of each year for five years and receive a return of 7%, how much is the annuity worth in today's dollars?

b.Now consider what happens if we increase the number of years of the annuity, from 5 to 6 years:

Before calculating, predict whether the present value of the annuity will rise or fall by more or less than $1000? Describe in a few sentences why this is the case.

Calculate how much is the annuity worth in today's dollars to confirm your prediction.

c. Now (going back to the original case in a) consider what happens if we increase the rate of return, from 7% to 8%:

Before calculating, predict if the present value of the annuity will rise or fall from your answer in a? Describe in a few sentences why this is the case.

Calculate how much is the annuity worth in today's dollars to confirm your prediction.

Future Value of an Annuity

You just turned 12 and you want $40,000 for college at the end of your 17th year. If you are to deposit the same amount at the end of each year of your age into a risk-free account with a 5% annual interest rate, compounded annually, how much should you invest each year?