A person borrows $10,000 and repays the loan at the rate of $2, 400 per year. The lender charges interest of 10% per year. Assuming the payments are made continuously and interest is compounded continuously (a pretty good approximation to reality for long-term loans), the amount M(t) of money (in dollars) owed t years after the loan is mace satisfies the differential equation
dM/dt = 1/10 M - 2400 and the initial condition M(0) = 10000.
(a) Solve this initial-value problem for M(t).
M(t) = -1400e^(r/10) + 2400
(b) How long does it take to pay off the loan? That is, at what time t is M(t) = 0? Give your answer (in years) in decimal form with at least 3 decimal digits.
3.80211 x years