Question

He equation A = 1750(1.04)t represents an account balance t years after the account was created. Which statement is correct? a The account balance will increase 4% each year. b The account balance will decrease 4% each year. c The account balance will increase 0.04% each year. d The account balance will decrease 0.04% each year.

Answer 1

The correct statement is A. The account balance will increase 4% each year.

Explanation:

Let's recall that 1.04 is the result of adding:

1 + 0.04 and, we can also write 0.04 as 4/100 or 4%,

in consequence,

1.04 = 1 + 4%, where we're increasing an additional 4%.

The correct statement is A. The account balance will increase 4% each year.

Answer 2

a The account balance will increase 4% each year.

Explanation:

The relationship between the account balance A and time t is given as

`\[A = 1750(1.04)t\]`

So the account balance after 1 year ( t=1 ) will be
`\[A = 1750(1.04)(1)\]`

The account balance after 2 years ( t=2 ) will be
`\[A = 1750(1.04)(2)\]`

The account balance after 3 years ( t=3 ) will be
`\[A = 1750(1.04)(3)\]`

So we can see that each year the account balance will increase by 1.04. In percentage terms , this corresponds to a 4% increase.

So among the given options, option a is the correct one.