Question

Present Values

Use Present Value Tables or your calculator to complete the requirements below.

You have an opportunity to purchase a government security that will pay $217,000 in 5 years.

Required:

Round your answers to the nearest cent, if rounding is required.

1. Calculate what you would pay for the security if the appropriate interest (discount) rate is 6% compounded annually.
$

2. Calculate what you would pay for the security if the appropriate interest (discount) rate is 10% compounded annually.
$

3. Calculate what you would pay for the security if the appropriate interest (discount) rate is 6% compounded semiannually.
$

Answer 1

(1)-The amount to be paid for the security if the appropriate interest (discount) rate is 6% compounded annually.

The amount to be paid for the security is the present value of $217,000 discounted at 6% for 5 years

Present Value = Future Value / (1 + r)ⁿ

= $217,000 / (1 + 0.06)⁵

= $217,000 / 1.3382256

= $162,155.02

(2) The amount to be paid for the security if the appropriate interest (discount) rate is 10% compounded annually.

The amount to be paid for the security is the present value of $217,000 discounted at 10% for 5 years

Present Value = Future Value / (1 + r)ⁿ

= $217,000 / (1 + 0.10)⁵

= $217,000 / 1.61051

= $134,739.93

(3)- The amount to be paid for the security if the appropriate interest (discount) rate is 6% compounded semiannually.

The amount to be paid for the security is the present value of $217,000 discounted at 3% for 10 years (Since the compounding is done semi-annually)

Present Value = Future Value / (1 + r)ⁿ

= $217,000 / (1 + 0.03)¹⁰

= $217,000 / 1.3439164

= $161,468.38