Question

Josie has $4,000 in an account that earns 5% in interest compounded annually.

To the nearest cent, how much interest will she earn in 1 year?

Answer 1

$200

Explanation:

Annual Compound Interest Formula

`\large \text{$ \sf I=P\left(1+r\right)^(t)-P $}`

where:

• I = total interest.
• P = principal amount.
• r = interest rate (in decimal form).
• t = time (in years).

Given:

• P = $4,000
• r = 5% = 0.04
• t = 1 year

Substitute the given values into the formula and solve for I:

`\implies \sf I=4000(1+0.05)^1-4000`

`\implies \sf I=4000(1.05)-4000`

`\implies \sf I=4200-4000`

`\implies \sf I=200`

Therefore, the amount of interest Josie will earn in 1 year is $200.

Answer 2

• Josie will earn $200.00 in 1 year

Explanation:

Given

• Investment P = 4000,
• Interest rate r = 5% = 0.05,
• Number of compounds n = 1,
• Time t = 1,
• Interest I = ?

Solution

Since n = 1, the equation for interest is:

• I = Pr

Find I

• I = 4000*0.05 = 200