Question

give you $1,000 per year for the next 10 1. Your grandmother has offered to give you $1,000 per year to what is the present value of this 10-year. $1.000 annuity discounted back to the present at 5 percent? What will be the present value if you received the $1,000 payment at the beginning of each year? 2. You are graduating from college at the end of this semester, and you have decided to invest $5000 a year for the next 45 years. If you earn 8% compounded annually on your investment. How much will you have when you retire in 45 years? How much will you have if your $5000 investment were made at the beginning of each year? 3. You plan to buy a property in Florida five years from today. To do this, you estimate that you will need $30,000 at that time for the purchase. You would like to accumulate these funds by making equal annual deposits in your saving account, which pays 10 percent annually. If you make your first deposit at the end of this year, and you would like to your account to reach $30,000 when the final deposit is made, what amount do you need to deposit annually?

Answer 1

1]

payment received at end of year

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment. This is $1,000

r = interest rate per period. This is 5%, or 0.05.

n = number of periods. This is 10.

PV of annuity = $1,000 * [1 - (1 + 0.05)^-10] / 0.05

PV of annuity = $7,721.73

payment received at beginning of year

PV of annuity due = P + (P * [1 - (1 + r)^-(n-1)] / r)

where P = periodic payment. This is $1,000

r = interest rate per period. This is 5%, or 0.05.

n = number of periods. This is 10.

PV of annuity due = $1,000 + ($1,000 * [1 - (1 + 0.05)^-(10-1)] / 0.05)

PV of annuity due = $8,107.82