Pregunta
- Erik needs to borrow
Loan
Loan Bc
a) Make an educated GUESS which loan would cost Erik less interest. Explain your choice. Mar!
are not given on the occuracy of your guess, but on how well you justify your choice. [2 marl
Loan
Loan Bc
a) Make an educated GUESS which loan would cost Erik less interest. Explain your choice. Mar!
are not given on the occuracy of your guess, but on how well you justify your choice. [2 marl
Ask by Floyd Grant. in Canada
Jan 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
a) Educated Guess:
Loan B would cost Erik less interest because it has a lower annual interest rate of 9.2% compared to Loan A’s 10%. Even though Loan B compounds more frequently (quarterly), the lower rate makes it the better choice.
Justification:
-
Lower Interest Rate: Loan B’s 9.2% is less than Loan A’s 10%, meaning Erik would pay less interest overall.
-
Compounding Frequency: Although Loan B compounds more often (quarterly), the difference in interest rates makes Loan B more economical.
Therefore, Loan B is expected to cost Erik less interest.
Solución
a) Educated Guess:
Loan B would cost Erik less interest.
Justification:
-
Lower Nominal Interest Rate: Loan B offers a 9.2% annual interest rate compared to Loan A’s 10%. A lower interest rate generally means less interest accrued over time.
-
Compounding Frequency: While Loan A compounds semi-annually (twice a year) and Loan B compounds quarterly (four times a year), which means Loan B compounds more frequently, the impact of the slightly higher compounding frequency is likely outweighed by the lower nominal rate.
-
Effective Interest Rate Consideration: Even without exact calculations, the lower nominal rate of Loan B suggests that its overall effective interest rate would be less than Loan A’s, resulting in less total interest paid over the three years.
Therefore, based on the lower interest rate and despite the higher compounding frequency, Loan B is expected to cost Erik less in interest.
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Simplifique esta solución Extra Insights
Loan A has a higher interest rate of 10% compared to Loan B’s 9.2%, which might suggest it’s more expensive. However, Loan A is compounded semi-annually, while Loan B is compounded quarterly. Generally, more frequent compounding can lead to higher interest costs over time, even with a lower interest rate. My educated guess would be that Loan B could end up costing Erik less interest because of the lower nominal rate, despite the more frequent compounding, but let’s crunch some numbers for the exact figures!
To clarify your guess, you might want to be mindful that compounding frequency plays a crucial role in the total cost of loans. Although Loan B has the lower interest rate, the quarterly compounding could lead to slightly higher costs when the total amount owed is calculated. To fully gauge which option Erik should choose, calculating the exact total repayments for both loans will reveal the true cost of each over three years!
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