Question

Each year caronline deposited a certain amount of money in an account which pays an annual interest rate of r so that at the end of each year, the balance in the account is multiplied by a growth factor of x=1+r. $600 is deposited at the start of the first year, and $200 at the start of the following year. Write an expression for a value of the account at the end of three years in terms of growth factors x. Find the value at the end of 3 years if the interest rate is 4%.

Answer 1

The balance in the account at the end of each year is given by the formula:

balance = previous balance * growth factor

At the start of the first year, the balance is 600$ and the growth factor is x = 1 + r. At the start of the second year, the balance is the value of the account at the end of the first year, and the growth factor is still x = 1 + r. At the start of the third year, the balance is the value of the account at the end of the second year, and the growth factor is still x = 1 + r.

Therefore, the balance at the end of three years can be expressed as:

balance = 600 * x * (200 * x)

If the interest rate is 4%, the growth factor is x = 1 + 0.04 = 1.04. Plugging this value into the equation for the balance, we find that the balance at the end of three years is:

balance = 600 * 1.04 * (200 * 1.04)
= 648 * 288
= 186368

So the balance at the end of three years is $186368.