An initial investment of $12,000 is invested for 2 years in an account that earns 4% interest compounded quarterly. Find the amount of mnoey in the account at the end of the period.
Well, when it comes to money, I'm no mathematician, but I can definitely give it a shot. Let's break it down.
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.
To find the amount of money in the account at the end of the period, we can use the formula for compound interest:
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.
To find the amount of money in the account at the end of the period, we can use the compound interest formula:
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.
P = Po(1+r)^n.
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.