You deposit $7,900 in a money-market account that pays an annual interest rate of 4.3%. The interest is compounded quarterly. How much money will you have after 3 years?
7900(1+.043/4)^(4*3) = 8981.57
To calculate the amount of money you will have after 3 years with quarterly compounding, you can use the formula for compound interest:
A = P(1 + r/n)^(nt),
where:
A is the final amount of money,
P is the principal (initial deposit),
r is the annual interest rate (as a decimal),
n is the number of times the interest is compounded per year, and
t is the number of years.
In this case, P = $7,900, r = 0.043 (4.3% expressed as a decimal), n = 4 (quarterly compounding), and t = 3.
Plugging these values into the formula, you get:
A = $7,900(1 + 0.043/4)^(4*3).
First, calculate the value in the parentheses:
1 + 0.043/4 = 1 + 0.01075 = 1.01075.
Next, raise this value to the power of (4*3):
(1.01075)^(4*3) = (1.01075)^12.
Using a calculator, you can find that (1.01075)^12 ≈ 1.1349.
Now, multiply this value by the principal P:
$7,900 * 1.1349 ≈ $8,959.09.
Therefore, after 3 years with quarterly compounding, you will have approximately $8,959.09 in your money-market account.