The balance of an investment is increasing according to the rule: Next year’s balance = 1.08 x current balance What is the constant percent increase per year? If the original balance of the investment was $2000 find a formula that gives the balance B (in dollars) after T years.

The constant percent increase per year is 8%.

In which B(0) is the initial amount and r is the growth rate, as a decimal.

Next year’s balance = 1.08 x current balance

So

This means that:

The constant percent increase per year is 8%

If the original balance of the investment was $2000 find a formula that gives the balance B (in dollars) after T years.

This means that

So

[tex]B(T) = 2000(1.08)^{T}{/tex]

Step-by-step explanation:

1. Rate of increase

 Let B = this year's balance. Then

1.08B = next year's balance

1.08B = B + 0.08B = B + 8 % of B

2. The formula

Each year, the balance is multiplied by 1.08.

The end of a year is the same as the end of the previous year.  

If T = the number of years, then the balance at the beginning of Year 1 is B₀.

If B₀ = $2000, the formula becomes