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When you borrow money to buy a house or a car, you pay off the loan in monthly payments, but the interest is always accruing on the outstanding balance. This makes the determination of your monthly payment on a loan more complicated than you might expect. If you borrow P dollars at a monthly interest rate of r (as a decimal) and wish to pay off the note in t months, then your monthly payment M = M(P,r,t) in dollars can be calculated using the following function. Pr(1+r) (1 + r)f - 1 M = The above function can be rearranged to show the amount of money P = P(M, r, t) as shown below, in dollars, that you can afford to borrow at a monthly interest rate of r (as a decimal) if you are able to make t monthly payments of M dollars. P = M x (1 + r)t Suppose you can afford to pay $300 per month for 2 years. (a) How much money can you afford to borrow for the purchase of a car if the prevailing monthly interest rate is 0.75%? (That is 9% APR.) Express the answer in functional notation, and then calculate it. (Round your amount to two decimal places.) P( m x )= $ 7660.8 (b) Suppose your car dealer can arrange a special monthly interest rate of 0.25% (or 3% APR). How much can you afford to borrow now? (Round your answer to two decimal places.) $ 8142.4 (c) Even at 3% APR you find yourself looking at a car you can't afford, and you consider extending the period during which you are willing to make payments to 3 years. How much can you afford to borrow under these conditions? (Round your answer to two decimal places.) $ 12026

When you borrow money to buy a house or a car, you pay off the loan in monthly payments, but the interest is always accruing on the outstanding balance. This makes the determination of your monthly payment on a loan more complicated than you might expect. If you borrow P dollars at a monthly interest rate of r (as a decimal) and wish to pay off the note in t months, then your monthly payment M = M(P,r,t) in dollars can be calculated using the following function. Pr(1+r) (1 + r)f - 1 M = The above function can be rearranged to show the amount of money P = P(M, r, t) as shown below, in dollars, that you can afford to borrow at a monthly interest rate of r (as a decimal) if you are able to make t monthly payments of M dollars. P = M x (1 + r)t Suppose you can afford to pay $300 per month for 2 years. (a) How much money can you afford to borrow for the purchase of a car if the prevailing monthly interest rate is 0.75%? (That is 9% APR.) Express the answer in functional notation, and then calculate it. (Round your amount to two decimal places.) P( m x )= $ 7660.8 (b) Suppose your car dealer can arrange a special monthly interest rate of 0.25% (or 3% APR). How much can you afford to borrow now? (Round your answer to two decimal places.) $ 8142.4 (c) Even at 3% APR you find yourself looking at a car you can't afford, and you consider extending the period during which you are willing to make payments to 3 years. How much can you afford to borrow under these conditions? (Round your answer to two decimal places.) $ 12026

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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When you borrow money to buy a house or a car, you pay off the loan in monthly payments, but the interest is always accruing on the outstanding balance. This makes the determination of your monthly payment on a loan more complicated than you might expect. If you borrow P dollars at a monthly interest rate of r (as a decimal) and wish to pay off the note in t months, then your monthly payment M = M(P,r,t) in dollars can be calculated using the following function. Pr(1+r)t M = (1 + r)* – 1 The above function can be rearranged to show the amount of money P = P(M, r, t) as shown below, in dollars, that you can afford to borrow at a monthly interest rate of r (as a decimal) if you are able to make t monthly payments of M dollars. P = M x . 1 - (1 + r)t Suppose you can afford to pay $300 per month for 2 years. (a) How much money can you afford to borrow for the purchase of a car if the prevailing monthly interest rate is 0.75%? (That is 9% APR.) Express the answer in functional notation, and then calculate it. (Round your amount to two decimal places.) P(r |x ) = $7660.8 (b) Suppose your car dealer can arrange a special monthly interest rate of 0.25% (or 3% APR). How much can you afford to borrow now? (Round your answer to two decimal places.) $ 8142.4 (c) Even at 3% APR you find yourself looking at a car you can't afford, and you consider extending the period during which you are willing to make payments to 3 years. How much can you afford to borrow under these conditions? (Round your answer to two decimal places.) $ 12026
Transcribed Image Text:When you borrow money to buy a house or a car, you pay off the loan in monthly payments, but the interest is always accruing on the outstanding balance. This makes the determination of your monthly payment on a loan more complicated than you might expect. If you borrow P dollars at a monthly interest rate of r (as a decimal) and wish to pay off the note in t months, then your monthly payment M = M(P,r,t) in dollars can be calculated using the following function. Pr(1+r)t M = (1 + r)* – 1 The above function can be rearranged to show the amount of money P = P(M, r, t) as shown below, in dollars, that you can afford to borrow at a monthly interest rate of r (as a decimal) if you are able to make t monthly payments of M dollars. P = M x . 1 - (1 + r)t Suppose you can afford to pay $300 per month for 2 years. (a) How much money can you afford to borrow for the purchase of a car if the prevailing monthly interest rate is 0.75%? (That is 9% APR.) Express the answer in functional notation, and then calculate it. (Round your amount to two decimal places.) P(r |x ) = $7660.8 (b) Suppose your car dealer can arrange a special monthly interest rate of 0.25% (or 3% APR). How much can you afford to borrow now? (Round your answer to two decimal places.) $ 8142.4 (c) Even at 3% APR you find yourself looking at a car you can't afford, and you consider extending the period during which you are willing to make payments to 3 years. How much can you afford to borrow under these conditions? (Round your answer to two decimal places.) $ 12026
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