Question

An account grows at an annual interest rate of r, so it grows by a factor of x= 1 + r each

year. The function A(x) = 800x* + 350x + 500x² + 600x gives the amount in the account
after 4 years when the growth factor is x.

Answer 1

The amount initially put (deposited) in the account is 800 + 350/x + 500/x² + 600/x³

Explanation:

The annual interest rate by which the account grows = r

The factor by which the account grows annually = 1 + r

The function that provides the amount in the account after 4 years, given that the growth factor is x is given as follows;

A(x) = 800·x⁴ + 350·x³ + 500·x² + 600·x

The amount, P, initially put (deposited) in the account is given as follows;

P × (x)⁴ = 800·x⁴ + 350·x³ + 500·x² + 600·x

P = (800·x⁴ + 350·x³ + 500·x² + 600·x)/(x⁴) = 800 + 350/x + 500/x² + 600/x³

P = 800 + 350/x + 500/x² + 600/x³

The amount initially put (deposited) in the account = 800 + 350/x + 500/x² + 600/x³