Question

Which of the following investments that pay $19,000 in five years will have a higher price today? Assume that both investments have equal risk. The security that earns an interest rate of 14.50% The security that earns an interest rate of 21.75% Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 6.80%. Assuming that both investments have equal risk and Eric's investment time horizon is flexible, which of the following investment options will exhibit the lower price? O An investment that matures in nine years O An investment that matures in eight years

Answer 1

Answer a.

Security with interest rate of 14.50%:

Present Value = Amount to be received / (1 + Interest Rate)^Period
Present Value = $19,000 / 1.1450^5
Present Value = $9,654.42

Security with interest rate of 21.75%:

Present Value = Amount to be received / (1 + Interest Rate)^Period
Present Value = $19,000 / 1.2175^5
Present Value = $7,102.46

So, security with an interest rate of 14.50% will price more today.

Answer b.

Investment that mature in nine years:

Present Value = Amount to be received / (1 + Interest Rate)^Period
Present Value = $1,000 / 1.0680^9
Present Value = $553.17

Investment that mature in eight years:

Present Value = Amount to be received / (1 + Interest Rate)^Period
Present Value = $1,000 / 1.0680^8
Present Value = $590.79

So, investment with 9 years to maturity will exhibit the lower price.

Answer c.

Annual deposit = $3,250
Interest rate = 9%
Number of deposits = 8

Accumulated Sum = $3,250*1.09^7 + $3,250*1.09^6 + ... + $3,250*1.09 + $3,250
Accumulated Sum = $3,250 * (1.09^8 - 1) / 0.09
Accumulated Sum = $3,250 * 11.02847
Accumulated Sum = $35,843