If instead you defer payment for 1 month, you pay \(P\) in 1 month.
So by delaying payment, you are effectively borrowing \(0.9525P\) for 1 month and paying back \(P\). The monthly interest rate is
\(\frac{P - 0.9525P}{0.9525P} =\)
\frac{0.0475P}{0.9525P}
\frac{0.0475}{0.9525} \approx 0.04987 ]
So the monthly rate is about \(4.987\%\).
The implicit annual borrowing rate, using a simple annualization, is
\(12 \times 4.987\% \approx 59.8\%\)
If compounded monthly, the effective annual rate is
\((1.04987)^{12} - 1 \approx 0.792\)
or about \(79.2\%\).
Answer:
Nominal annual rate: about \(59.8\%\)
Effective annual rate: about \(79.2\%\)
If this is for a typical finance class, they usually want the effective monthly rate first, and then often the nominal annual rate \(= 59.8\%\). ```
Mark Florkowski
Team
That is improper formatting by the model, it used inline inconsistently and did not properly encapsulate the LaTeX sections. The correct LaTeX would be
```
Let the full price be (P).
If you pay cash today, you pay only
(0.9525P)
because of the (4.75%) discount.
If instead you defer payment for 1 month, you pay (P) in 1 month.
So by delaying payment, you are effectively borrowing (0.9525P) for 1 month and paying back (P). The monthly interest rate is
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Comments2
Tan Milkshake
Additional example:
```
Let the full price be \(P\).
If you pay cash today, you pay only
\(0.9525P\)
because of the \(4.75\%\) discount.
If instead you defer payment for 1 month, you pay \(P\) in 1 month.
So by delaying payment, you are effectively borrowing \(0.9525P\) for 1 month and paying back \(P\). The monthly interest rate is
\(\frac{P - 0.9525P}{0.9525P} =\)
\frac{0.0475P}{0.9525P}
\frac{0.0475}{0.9525}
\approx 0.04987
]
So the monthly rate is about \(4.987\%\).
The implicit annual borrowing rate, using a simple annualization, is
\(12 \times 4.987\% \approx 59.8\%\)
If compounded monthly, the effective annual rate is
\((1.04987)^{12} - 1 \approx 0.792\)
or about \(79.2\%\).
Answer:
Nominal annual rate: about \(59.8\%\)
Effective annual rate: about \(79.2\%\)
If this is for a typical finance class, they usually want the effective monthly rate first, and then often the nominal annual rate \(= 59.8\%\).
```
Mark Florkowski
That is improper formatting by the model, it used inline inconsistently and did not properly encapsulate the LaTeX sections. The correct LaTeX would be
```
Let the full price be (P).
If you pay cash today, you pay only
(0.9525P)
because of the (4.75%) discount.
If instead you defer payment for 1 month, you pay (P) in 1 month.
So by delaying payment, you are effectively borrowing (0.9525P) for 1 month and paying back (P). The monthly interest rate is
$$ \frac{P - 0.9525P}{0.9525P} = \frac{0.0475P}{0.9525P} = \frac{0.0475}{0.9525} \approx 0.04987 $$
So the monthly rate is about (4.987%).
The implicit annual borrowing rate, using a simple annualization, is
(12 \times 4.987% \approx 59.8%)
If compounded monthly, the effective annual rate is
((1.04987)^{12} - 1 \approx 0.792)
or about (79.2%).
Answer:
Nominal annual rate: about (59.8%)
Effective annual rate: about (79.2%)
If this is for a typical finance class, they usually want the effective monthly rate first, and then often the nominal annual rate (= 59.8%).
```