Angela invests $2,550 at 3% interest compounded annually. What will be the balance in the account after 1.5 years?
(1 point)
$2,626.50 $3,635.69 $2,665.61 $4,792.50
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this case, we have:
P = $2,550
r = 0.03 (3% as a decimal)
n = 1 (compounded annually)
t = 1.5 years
Plugging these values into the formula, we get:
A = $2,550(1 + 0.03/1)^(1*1.5)
A = $2,665.61
Therefore, the balance in the account after 1.5 years will be $2,665.61.
The answer is option C: $2,665.61.
To calculate the balance in the account after 1.5 years, we need to use the compound interest formula:
A = P(1 + r/n)^(nt),
where:
A = the future balance
P = principal amount ($2,550)
r = annual interest rate (3% or 0.03)
n = number of times interest is compounded per year (annual compounding, so n = 1)
t = time in years (1.5 years).
Plugging in the values, we have:
A = 2550(1 + 0.03/1)^(1*1.5)
A = 2550(1 + 0.03)^(1.5)
A = 2550(1.03)^(1.5)
A ≈ 2550(1.030301)
A ≈ 2626.55.
Therefore, the balance in the account after 1.5 years will be approximately $2,626.55.
The closest option to the calculated balance is $2,626.50.
To find the balance in the account after 1.5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the balance after time t
P = the principal amount (initial investment)
r = the annual interest rate (written as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = $2,550
r = 3% or 0.03 (converted to a decimal)
n = 1 (compounded annually)
t = 1.5 years
We can now plug in the values into the formula:
A = $2,550(1 + 0.03/1)^(1 * 1.5)
Simplifying the equation:
A = $2,550(1 + 0.03)^(1.5)
Calculating the values inside the parentheses:
A = $2,550(1.03)^(1.5)
Using a calculator to evaluate the expression:
A ≈ $2,550(1.03045)
A ≈ $2,625.61
Therefore, the balance in the account after 1.5 years will be approximately $2,625.61.
None of the given options match the calculated value, so it seems there might be a mistake in the provided answer choices.