Arkady invests $2000 in an account paying 6% annual interest.(a) If the interest is compou...

Arkady invests $2000 in an account paying 6% annual interest.

(a) If the interest is compounded continuously and no additional deposits or withdrawals are made, how much will be in the account at the end of 10 years?

(b) If the interest is awarded in discrete annual packets, then you want to use the discrete formula generated in Exercise. In this case, m = 1, so

The recursive definition,

is called a first-order difference equation and generates the sequence

A little simplification shows that the nth term of this sequence is

Now suppose that I represents the annual interest rate, but the interest is awarded in discrete packets, m times per year. Then the rate awarded during each compounding period is I/ m. Consequently, if the initial investment is P0, the balance is P0(1 + I/m) at the end of the first compounding period, P0(l+I/m)2 at the end of the second compounding period, and so on.

(a) Give a first-order difference equation with an initial condition that generates a sequence describing the balance in the account at the end of each compounding period.

(b) Find a formula for the nth term of the sequence generated by the first-order difference equation created in part (a).

Calculate the balance in the account at the end of the 10-year period if the interest is compounded

· semiannually (twice per year)

· monthly (12 times per year)

· daily (365 times per year)

(c) Write a short paragraph explaining the point of this problem.