Money in a bank account grows continuously at an annual rate of r (assume r is t

Question

Money in a bank account grows continuously at an annual rate of r (assume r is theinterest rate in decimal form). Suppose $4300 is put o an account in 2010. Write a differential equation satisfied by M, the amount of money in the account at time t, measured in years since 2010. dM/dt = Solve the initial value problem. Your answer will still have r in it. M(t) = How much more money would be in the account at the end of 4 years if theinterest rate was 10% instead of 5%. Round your answer to two decimal places. $ .

Explanation / Answer

a) dM / dt = interest = r M , M(0) = 4300.

b) lnM = rt + A......where A = M(0)

M = Ae^rt = 4300 e^rt

c) At interest = 5 % , M = 4300 e^ 0.05 * 4 = 4300 e^0.2 = 4300 * 1.222 = 5254.6

At interest = 10 % , M= 4300 e^0.1 *4 = 4300 e^0.4 = 4300 * 1.4918 = 6414.74

so more money = 6414.74 - 5254.6 = 1160.14

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