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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 tha 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. 1 + - (₁ - (+²²) 1 P = M x = x (1 + r) ² 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 tw decimal places.) PC = $ (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.) $ (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.)

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 tha 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. 1 + - (₁ - (+²²) 1 P = M x = x (1 + r) ² 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 tw decimal places.) PC = $ (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.) $ (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.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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 tha 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)* (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 + r)t P = M x ¹ x 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 tw decimal places.) PC| = $ (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.) $ (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.)
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 tha 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)* (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 + r)t P = M x ¹ x 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 tw decimal places.) PC| = $ (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.) $ (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.)
According to data about movie ticket prices, between 2000 and 2014 the average cost of a movie ticket in a given year was C(t) = 5.20 +0.24t dollars. Here t is the time in years since 2000. (a) Explain in practical terms the meaning of C(9). The expression C(9) is the average cost, in dollars, of a movie ticket in 2014. The expression C(9) is the year in which a movie ticket will cost 9 dollars more than a movie in 2000 cost. The expression C(9) is the year in which a movie ticket will cost 9 dollars. The expression C(9) is the average cost, in dollars, of a movie ticket in 2009. The expression C(9) is the average cost, in dollars, of a movie ticket in 2000. (b) Use functional notation to express the average cost of a movie ticket in 2013. 9 (c) Calculate the average cost of a movie ticket in 2013. $ 7.36 X
Transcribed Image Text:According to data about movie ticket prices, between 2000 and 2014 the average cost of a movie ticket in a given year was C(t) = 5.20 +0.24t dollars. Here t is the time in years since 2000. (a) Explain in practical terms the meaning of C(9). The expression C(9) is the average cost, in dollars, of a movie ticket in 2014. The expression C(9) is the year in which a movie ticket will cost 9 dollars more than a movie in 2000 cost. The expression C(9) is the year in which a movie ticket will cost 9 dollars. The expression C(9) is the average cost, in dollars, of a movie ticket in 2009. The expression C(9) is the average cost, in dollars, of a movie ticket in 2000. (b) Use functional notation to express the average cost of a movie ticket in 2013. 9 (c) Calculate the average cost of a movie ticket in 2013. $ 7.36 X
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