Question

Question 2
What is the present value (i.e., price) today of a bond that will pay its owner
$
1
,
000
,
000
$1,000,000 five years from today if the discount rate is
4
%
4% per annum?

(This is called a zero-coupon or pure discount bond)


821
,
927.11
821,927.11



1
,
000
,
000
1,000,000



1
,
216
,
652.90
1,216,652.90



40
,
000
40,000

Answer 1

To calculate the present value of a zero-coupon bond that will pay $1,000,000 in five years, we can use the present value formula:

\[
PV = \frac{FV}{(1 + r)^n}
\]

where:
- \( PV \) is the present value,
- \( FV \) is the future value ($1,000,000),
- \( r \) is the discount rate (4% or 0.04), and
- \( n \) is the number of years until maturity (5 years).

Plugging in the values:

\[
PV = \frac{1,000,000}{(1 + 0.04)^5}
\]

Calculating \( (1 + 0.04)^5 \):

\[
(1.04)^5 \approx 1.2166529
\]

Now, substituting this back into the formula:

\[
PV = \frac{1,000,000}{1.2166529} \approx 821,927.11
\]

Thus, the present value (price) today of the bond is approximately **$821,927.11**.

So, the correct answer is:

**821,927.11**