Question

Suppose you invest $1,000 in a financial asset earning an annual interest rate of 6%.

1. How much interest will you earn after one year? How much money will be available to you (principal and interest) at the end of one year?
2. If the money is allowed to compound annually at 6%, how much money will be available at the end of 2 years? 5 years?
3. Suppose you have the opportunity to purchase a risk-free asset that will return $1,000 one year from now. If the risk-free interest rate is currently 5%, what is the present value of this asset?
4. Alternatively, suppose the risk-free asset will return $1,000 two years from now. Still assuming a risk-free interest rate of 5%, what is the present value of this asset?
5. You are considering purchasing a risk-free asset that will return $1,000 at the end of one year, another $1,000 at the end of the second year, and another $1,000 at the end of the third year. What is present value of this asset if the risk-free interest rate is 5%?
6. Why does the present value of an asset tell you the greatest amount you should pay for the asset?

Answer 1

Solution :-

Interest Earn in One Year = $1,000 * 6% = $60

Money available at the end of Year = $1,000 * ( 1 + 0.06 ) = $1,060

The Money Available at the end of 2 Years = $1,000 * ( 1 + 0.06 )² = $1,123.6

The Money Available at the end of 5 Years = $1,000 * ( 1 + 0.06 )⁵ = $1,338.23

Present Value of Asset of $1,000 after one year = $1,000 / ( 1 + 0.05 ) = $952.38

Present Value of Asset of $1,000 after two year = $1,000 / ( 1 + 0.05 )² = $907.03

Present Value = Cash flow per year * PVAF(5% , 3) = $1000 * 2.723 = $2,723.25