Question
On January 1,1998, Moon Corporation sold a motor vehicle to Sun Company. Sun signed a Br.
200,000 non-interest bearing promissory note due on January 1, 2001. The prevailing interest rate for a
similar note on January 1, 1998, was 9%. How much is the selling price of the motor vehicle for Moon
Corporation?
200,000 non-interest bearing promissory note due on January 1, 2001. The prevailing interest rate for a
similar note on January 1, 1998, was 9%. How much is the selling price of the motor vehicle for Moon
Corporation?
Answers
GPT-4o mini
To determine the present value (selling price) of the non-interest bearing promissory note, we can calculate it using the formula for the present value of a single sum:
\[
PV = \frac{FV}{(1 + r)^n}
\]
Where:
- \( PV \) is the present value (selling price of the motor vehicle).
- \( FV \) is the future value (the amount of the note, Br. 200,000).
- \( r \) is the interest rate (9% or 0.09).
- \( n \) is the number of years until the note matures (3 years).
Substituting the values:
\[
PV = \frac{200,000}{(1 + 0.09)^3}
\]
Calculating the denominator:
\[
(1 + 0.09)^3 = 1.09^3 \approx 1.295029
\]
Now calculate \( PV \):
\[
PV = \frac{200,000}{1.295029} \approx 154,031.71
\]
Thus, the selling price of the motor vehicle for Moon Corporation is approximately **Br. 154,031.71**.
\[
PV = \frac{FV}{(1 + r)^n}
\]
Where:
- \( PV \) is the present value (selling price of the motor vehicle).
- \( FV \) is the future value (the amount of the note, Br. 200,000).
- \( r \) is the interest rate (9% or 0.09).
- \( n \) is the number of years until the note matures (3 years).
Substituting the values:
\[
PV = \frac{200,000}{(1 + 0.09)^3}
\]
Calculating the denominator:
\[
(1 + 0.09)^3 = 1.09^3 \approx 1.295029
\]
Now calculate \( PV \):
\[
PV = \frac{200,000}{1.295029} \approx 154,031.71
\]
Thus, the selling price of the motor vehicle for Moon Corporation is approximately **Br. 154,031.71**.