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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. M = Pr (1+r)t (1 + r)² - 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. 1 - - - - - (1 - 1 + ²) 1 (1 r) P=Mx Suppose you can afford to pay $300 per month for 3 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 X (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 X X (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 4 years. How much can you afford to borrow under these conditions? (Round your answer to two decimal places.) $ 12035.26 X

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. M = Pr (1+r)t (1 + r)² - 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. 1 - - - - - (1 - 1 + ²) 1 (1 r) P=Mx Suppose you can afford to pay $300 per month for 3 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 X (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 X X (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 4 years. How much can you afford to borrow under these conditions? (Round your answer to two decimal places.) $ 12035.26 X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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. M = Pr (1+r)t (1 + r)² - 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. 1 - - - - - (1 - 1 + ²) 1 (1 r) P=Mx Suppose you can afford to pay $300 per month for 3 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 X (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 X X (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 4 years. How much can you afford to borrow under these conditions? (Round your answer to two decimal places.) $ 12035.26 X
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. M = Pr (1+r)t (1 + r)² - 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. 1 - - - - - (1 - 1 + ²) 1 (1 r) P=Mx Suppose you can afford to pay $300 per month for 3 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 X (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 X X (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 4 years. How much can you afford to borrow under these conditions? (Round your answer to two decimal places.) $ 12035.26 X
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