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A young man borrows $50,000 to buy a car. The lender charges an annual interest of 2% compounded yearly. The young man pays $k annually towards the loan. (a) Show that the ODE describing this loan is as follows: ds=k, where S=remaining loan ($), t-time (years) 50 dt - (b) By solving the ODE in (a), and applying the relevant conditions, determine the annual payment ($k), corrected to the nearest cent, required to pay off the loan completely in 5 years. (c) Write down the equation of S in terms of t, and sketch the graph of S vs t.

A young man borrows $50,000 to buy a car. The lender charges an annual interest of 2% compounded yearly. The young man pays $k annually towards the loan. (a) Show that the ODE describing this loan is as follows: ds=k, where S=remaining loan ($), t-time (years) 50 dt - (b) By solving the ODE in (a), and applying the relevant conditions, determine the annual payment ($k), corrected to the nearest cent, required to pay off the loan completely in 5 years. (c) Write down the equation of S in terms of t, and sketch the graph of S vs t.

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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Question 1 A young man borrows $50,000 to buy a car. The lender charges an annual interest of 2% compounded yearly. The young man pays $k annually towards the loan. (a) Show that the ODE describing this loan is as follows: ds S - k, where S=remaining loan ($), t-time (years) = dt 50 (b) By solving the ODE in (a), and applying the relevant conditions, determine the annual payment ($k), corrected to the nearest cent, required to pay off the loan completely in 5 years. (c) Write down the equation of S in terms of t, and sketch the graph of S vs t.
Transcribed Image Text:Question 1 A young man borrows $50,000 to buy a car. The lender charges an annual interest of 2% compounded yearly. The young man pays $k annually towards the loan. (a) Show that the ODE describing this loan is as follows: ds S - k, where S=remaining loan ($), t-time (years) = dt 50 (b) By solving the ODE in (a), and applying the relevant conditions, determine the annual payment ($k), corrected to the nearest cent, required to pay off the loan completely in 5 years. (c) Write down the equation of S in terms of t, and sketch the graph of S vs t.
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