Question

Apply problem solving methods and analyze solution of financial problems.

1.) You deposit $100 into an account earning a 10% annual rate of interest. How much money will you have in the account at the end of five years?

2.) You have just won the lottery and have a choice of receiving a lump sum of $1,000,000 or an annuity of $100,000 per year for 15 years. If the appropriate discount rate is 8%, which alternative would you choose? Explain.

3.) What happens to the future value of a sum of money deposited for N years as the rate of return k increases? What happens to the present value of a sum of money to be received at the end of N years as k increases?

Answer 1

Question 1:

PV = Deposit Amount = $100

r = annual rate of interest = 10%

n = 5 years

Account balance in 5 years = PV * (1+r)^n

= $100 * (1+10%)^5

= $100 * 1.61051

= $161.051

Therefore, balance in the account in 5 years is $161.05

Question 2:

Option a:

Lump sum payment = $1,000,000

Option b:

P = annual receipt = $100,000

n = 15 years

r = discount rate = 8%

Present Value of future cash flows = P * [1 - (1+r)^-n] / r

= $100,000 * [1 - (1+8%)^-15] / 8%

= $100,000 * 0.684758295 / 0.08

= $855,947.869

= $855,947.87

It is bettet to accept lump sum amount of $1,000,000 today

Question 3:

What happens to the future value of a sum of money deposited for N years as the rate of return k increases - Future value will increase as future value and rate of interest has positive relationship

FV = Sum Deposited * (1+r)^n

What happens to the present value of a sum of money to be received at the end of N years as k increases

Present value will increase as present value and rate of interest has inverse relationship

PV = Sum to be received / (1+r)^n