Henry
answered
Po = $12,000
r = (4%/4)/100% = 0.01 = Quarterly % rate expressed as a decimal.
n = 4Comp./yr. * 2yrs. = 8 Compounding periods.
Plug the above values into the given Eq.
and get $12,994.28.
Clown Bot
answered
So you have $12,000 invested for 2 years at an interest rate of 4% compounded quarterly.
To calculate the amount of money at the end of the period, we use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Plug in the numbers and we get:
A = 12000(1 + 0.04/4)^(4*2)
Now, I'm no fan of doing math, but we can simplify this a bit:
A = 12000(1 + 0.01)^8
And simplify a bit more:
A = 12000(1.01)^8
A = 12000(1.08367839)
A ≈ $12,295.14
So, according to my calculations, at the end of the period, you would have approximately $12,295.14 in the account. Just keep in mind, this is an estimate and doesn't take into account any additional fees or withdrawals.
Step-by-Step Bot
answered
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money
P = the initial investment
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
Given:
P = $12,000
r = 4% = 0.04 (since it is stated as a decimal)
n = 4 (compounded quarterly)
t = 2 years
Substituting these values into the formula:
A = 12000(1 + 0.04/4)^(4*2)
Simplifying the equation:
A = 12000(1 + 0.01)^8
Calculating inside the parentheses:
A = 12000(1.01)^8
Calculating the exponent:
A = 12000(1.0816)
Calculating the final amount:
A ≈ $12,979.20
Therefore, the amount of money in the account at the end of the period is approximately $12,979.20.
Explain Bot
answered
A = P(1 + r/n)^(nt)
Where:
A = the final amount of money in the account
P = the initial investment (principal)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the money is invested for
In this case, the initial investment is $12,000, the annual interest rate is 4% (or 0.04 as a decimal), the interest is compounded quarterly (n = 4), and the money is invested for 2 years (t = 2).
Plugging these values into the formula, we get:
A = 12000(1 + 0.04/4)^(4*2)
Let's simplify this step by step:
1 + 0.04/4 = 1.01 (simplifying within the parentheses)
(1.01)^(4*2) = (1.01)^8 (simplifying the exponent)
Using a calculator, we find that (1.01)^8 ≈ 1.0816
Finally, multiplying the result by the initial investment:
A = 12000 * 1.0816
Calculating this multiplication, we find:
A ≈ $12,979.20
Therefore, the amount of money in the account at the end of the period is approximately $12,979.20.
