Essentials Of Investments
11th Edition
ISBN: 9781260013924
Author: Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher: Mcgraw-hill Education,
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Suppose you make a charge of $1000 to a new credit card, but then charge nothing else and make the minimum payment each month. If the finance charges amount to a monthly rate of 1% and the minimum payment is 7% of the new balance, then your balance \( B \), in dollars, after \( n \) payments is an exponential function given by the following formula.
\[ B = 1000 \times a^n \]
Here the decay factor \( a \) is obtained from the finance charge and the minimum payment as shown in the following formula.
\[ a = (1 + 0.01)(1 - 0.07) \]
**(a)** Find the exact value of the decay factor \( a \). (Round your answer to three decimal places.)
\[ \boxed{} \times \]
**(b)** By what percentage does your balance decrease each month? (Round your answer to one decimal place.)
\[ \boxed{} \, \% \]
**(c)** What will your balance be after you have made payments for 2 years? (Round your answer to two decimal places.)
\[ \$\boxed{} \]
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Transcribed Image Text:**Text Transcription for Educational Website:**
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Suppose you make a charge of $1000 to a new credit card, but then charge nothing else and make the minimum payment each month. If the finance charges amount to a monthly rate of 1% and the minimum payment is 7% of the new balance, then your balance \( B \), in dollars, after \( n \) payments is an exponential function given by the following formula.
\[ B = 1000 \times a^n \]
Here the decay factor \( a \) is obtained from the finance charge and the minimum payment as shown in the following formula.
\[ a = (1 + 0.01)(1 - 0.07) \]
**(a)** Find the exact value of the decay factor \( a \). (Round your answer to three decimal places.)
\[ \boxed{} \times \]
**(b)** By what percentage does your balance decrease each month? (Round your answer to one decimal place.)
\[ \boxed{} \, \% \]
**(c)** What will your balance be after you have made payments for 2 years? (Round your answer to two decimal places.)
\[ \$\boxed{} \]
Need Help? [Read It]
---
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