I really need help with this problem I am not getting it at all anyhelp would be great thanks
What would be the amount of compound interest on $8,000 invested for one year at 6% compounded quarterly ?
Interest= 8000(1+.06/4)4 - 8000
http://math.about.com/library/weekly/aa042002a.htm
1st quarter:
$8,000 * 0.06 = $480.
$480 / 4 = $120 Interest for 1st quarter
2nd quarter:
$8,000 + $120 = $8,120
$8,120 * 0.06 = $487.20
$487.20 / 4 = $121.80 Interest for 2nd quarter
3rd quarter:
$8,120 + $121.80 = $8,241.80
I think you can finish the 3rd quarter and do the 4th quarter on your own.
We'll be glad to check your answer.
Of course, I can help you with that! To solve this problem, we'll need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (including principal and interest)
P = the principal amount (the initial investment)
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $8,000, the annual interest rate (r) is 6% (or 0.06 as a decimal) and the interest is compounded quarterly, which means it's compounded 4 times a year (n = 4). The time (t) is 1 year.
Now, let's substitute these values into the formula and calculate the amount of compound interest:
A = $8,000(1 + 0.06/4)^(4*1)
A = $8,000(1 + 0.015)^4
A = $8,000(1.015)^4
A = $8,000 * 1.061601
A ≈ $8,492.81 (rounded to two decimal places)
To find the amount of compound interest, we need to subtract the principal amount from the final amount:
Interest = $8,492.81 - $8,000
Interest ≈ $492.81
Therefore, the amount of compound interest on $8,000 invested for one year at 6% compounded quarterly is approximately $492.81.