please help how do you figure out the compound interest on $8,000 invested for one year at 6% compounded quarterly. rounded to the nearest dollar
1.5% (1/4 of 6%) interested is added each quarter. After four quarters, the value of the account is
8000*(1.015)^4 = $8491.
If interest had been compounded annually instead of quarterly, then the amount at the end of one year would be 8000*1.06 = $8480.
To calculate compound interest, you need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of compounding periods in a year
t = the number of years
In this case, the principal (P) is $8,000, the annual interest rate (r) is 6% or 0.06, and the investment is made for one year (t = 1). The interest is compounded quarterly, so there are 4 compounding periods per year (n = 4).
Let's plug these values into the formula:
A = 8000 * (1 + 0.06/4)^(4*1)
First, simplify inside the parentheses:
A = 8000 * (1 + 0.015)^(4)
Next, calculate the exponent:
A = 8000 * (1.015)^(4)
Now, evaluate the exponential term:
A = 8000 * (1.06136)
Finally, calculate the future value:
A = 8000 * 1.06136 = $8,490.88
Rounded to the nearest dollar, the compound interest on $8,000 invested for one year at 6% compounded quarterly is $8,491.