Question

The amount of money deposited into an account in a given year is multiplied by a growth factor of x = 1 + r. $800 is

deposited at the start of the first year; an additional $300 is deposited at the start of the next year, and $625 at the start of
the following year. Write an expression that represents the amount of money in the account at the end of the three years.

Answer 1

800(1 + r)³ + 300(1 + r)² + 625(1 + r)

Explanation:

At the beginning of the first year $800 is deposited.

At the end of the first year the amount of money in account = $800 × growth factor = 800(1 + r)

At the beginning of the second year, $300 is deposited, the money in account = 800(1 + r) + 300

At the end of the second year the amount of money in account is multiplied by growth factor. = [800(1 + r) + 300] × 1 + r = 800(1 + r)² + 300(1 + r)

At the beginning of the third year, $625 is deposited, the money in account = 800(1 + r)² + 300(1 + r) + 625

At the end of third year the money = [800(1 + r)² + 300(1 + r) + 625] × 1 + r = 800(1 + r)³ + 300(1 + r)² + 625(1 + r)