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 x a" 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.) (b) By what percentage does your balance decrease each month? (Round your answer to one decimal place.) (c) What will your balance be after you have made payments for 2 years? (Round your answer to two decimal places.) $ Need Help? Read It
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 x a" 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.) (b) By what percentage does your balance decrease each month? (Round your answer to one decimal place.) (c) What will your balance be after you have made payments for 2 years? (Round your answer to two decimal places.) $ Need Help? Read It
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![**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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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]
---
There are no graphs or diagrams included in the image.
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