Question

Suppose you receive ?$130 at the end of each year for the next three years.

a. If the interest rate is 7%?, what is the present value of these cash? flows?

b. What is the future value in three years of the present value you computed in ?(a?)?

c. Suppose you deposit the cash flows in a bank account that pays 7 % interest per year. What is the balance in the account at the end of each of the next three years? (after your deposit is? made)? How does the final bank balance compare with your answer in ?(b?)?

2. You have just received a windfall from an investment you made in a? friend's business. She will be paying you $14,425 at the end of this? year,$28,850 at the end of next? year, and $43,275

at the end of the year after that? (three years from? today). The interest rate is 8.4% per year.

a. What is the present value of your? windfall?

b. What is the future value of your windfall in three years? (on the date of the last? payment)?

3. What is the present value of $9,000 paid at the end of each of the next 87 years if the interest rate is 12% per? year?

Answer 1

1) a) Present value of an amount is computed as -

PV = Amount / (1 + r)ⁿ

where, r = rate of interest, n = no. of years

PV = [ $130 / (1 + 0.07)¹ ] + [ $130 / (1 + 0.07)² ] + [ $130 / (1 + 0.07)³ ] = $341.16108577413

b) Future value of an amount is computed as -

FV = Amount x (1 + r)ⁿ

or, FV = $341.16108577413 x (1 + 0.07)³ = $417.94

c) First year

Balance = $130

Second year

Balance = $130 x 1.07 + $130 = $269.10

Third year

Balance = $269.10 x 1.07 + $130 = $417.937 or $417.94

The ending balance is same as part b.

2) a) PV = [ $14,425 / (1 + 0.084)¹ ] + [ $28,850 / (1 + 0.084)² ] + [ $43,275 / (1 + 0.084)³ ] = $71,833.416208136

b) FV = $71,833.416208136 x (1 + 0.084)³ = $91,498.58

3) Present value of equal annual amounts or annuity can be computed as -