1. Suppose that you borrow $10,00 at a continuous interest rate of 4%. You plan to repay the loan in continuous payments of k dollars per year. Let B denote the balance remaining to be paid on the loan in dollars and t be the time in years since the loan started. a. Explain why B, t and k satisfy the initial value problem dB = 0.04 B – k, B(0) = 10,000 dt b. Solve the differential equation c. What should the value of k be if you want to pay the loan off in 5 years. d. How much total interest will you pay over the life of the loan if you make these payments over 5 years? e. Suppose instead that you pay the loan off over 10 years. What is your yearly payment and how much total interest do you pay?
1. Suppose that you borrow $10,00 at a continuous interest rate of 4%. You plan to repay the loan in continuous payments of k dollars per year. Let B denote the balance remaining to be paid on the loan in dollars and t be the time in years since the loan started. a. Explain why B, t and k satisfy the initial value problem dB = 0.04 B – k, B(0) = 10,000 dt b. Solve the differential equation c. What should the value of k be if you want to pay the loan off in 5 years. d. How much total interest will you pay over the life of the loan if you make these payments over 5 years? e. Suppose instead that you pay the loan off over 10 years. What is your yearly payment and how much total interest do you pay?
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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Transcribed Image Text:1. Suppose that you borrow $10,00 at a continuous interest rate of 4%. You plan to repay the loan in
continuous payments of k dollars per year. Let B denote the balance remaining to be paid on the
loan in dollars and t be the time in years since the loan started.
a. Explain why B, t and k satisfy the initial value problem
dB
= 0.04 B – k, B(0) = 10,000
dt
b. Solve the differential equation
c. What should the value of k be if you want to pay the loan off in 5 years.
d. How much total interest will you pay over the life of the loan if you make these payments over
5 years?
e. Suppose instead that you pay the loan off over 10 years. What is your yearly payment and how
much total interest do you pay?
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