A bad loan Consider a loan repayment plan described by theinitial value problem B'(t) = 0.03B - 600, B(0) = 40,000,where the amount borrowed is B(0) = $40,000, the monthly payments are $600, and B(t) is the unpaid balance in the loan.a. Find the solution of the initial value problem and explain whyB is an increasing function.b. What is the most that you can borrow under the terms of thisloan without going further into debt each month? c. Now consider the more general loan repayment plan describedby the initial value problem B'(t) = rB - m, B(0) = B0,where r > 0 reflects the interest rate, m > 0 is the monthlypayment, and B0 > 0 is the amount borrowed. In terms ofm and r, what is the maximum amount B0 that can be borrowedwithout going further into debt each month?
A bad loan Consider a loan repayment plan described by the
initial value problem
B'(t) = 0.03B - 600, B(0) = 40,000,
where the amount borrowed is B(0) = $40,000, the monthly payments are $600, and B(t) is the unpaid balance in the loan.
a. Find the solution of the initial value problem and explain why
B is an increasing function.
b. What is the most that you can borrow under the terms of this
loan without going further into debt each month? c. Now consider the more general loan repayment plan described
by the initial value problem
B'(t) = rB - m, B(0) = B0,
where r > 0 reflects the interest rate, m > 0 is the monthly
payment, and B0 > 0 is the amount borrowed. In terms of
m and r, what is the maximum amount B0 that can be borrowed
without going further into debt each month?
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