Write down the sum that gives the balance after 5 years

Question

Question: (Continuation of Problem) Now suppose the money is deposited once a month (instead of continuously) but still at a rate of $1200 per year.

(a) Write down the sum that gives the balance after 5 years, assuming the first deposit is made one month from today, and today is t = 0.

(b) The sum you wrote in part (a) is a Riemann sum approximation to the integral

₀∫⁵ 1200e^0.1tdt

Determine whether it is a left sum or right sum, and determine what Δt and n are. Then use your calculator to evaluate the sum.

(c) Compare your answer in part (b) to your answer to Problem (c).

Problem: A bank account earns 5% annual interest, compounded continuously. Money is deposited in a continuous cash flow at a rate of $1200 per year into the account.

(a) Write a differential equation that describes the rate at which the balance B = f(t) is changing.

(b) Solve the differential equation given an initial balance B0 = 0.

(c) Find the balance after 5 years.