please check my answer thanks
What would be the amount of compound interest on $ 8,000 invested for one year at 6 %, compounded quarterly ? (need to show all of your work )
ok this is what I got
$8,000 x 0.6 = $ 480
$ 480 / 4 = $120
$120 x 0.6 / 4 = $ 121.80
$8,241.80 x 0.6 /4 =$ 123 .63
$8,365 .43 x0.6 / 4 = 125.48
$ 8,491
please let me know if I am right thanks again
correct
You can do the calculations above in one step using the formula
Amount = Principal (1+i)^n , where i is the periodic interest rate, in this case per quarter year,
and n is the number of interest periods , in this case n=4
so Amount = 8000(1.015)^4
= 8490.91
I also noticed in your solutions that you used .6 for 6%, that should have been .06
I am sure you are not expected to do it the way you attempted it.
That would be totally impractical had the time been something like 10 years.
To calculate compound interest, you use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Let's break down the calculation step by step using the given information:
1. Principal amount (P): $8,000
2. Annual interest rate (r): 6% or 0.06 in decimal form
3. Number of times interest is compounded per year (n): quarterly (4 times per year)
4. Number of years (t): 1 year
First, we need to determine the interest rate per compounding period:
Interest rate per period (i) = r/n
i = 0.06/4 = 0.015
Now, let's calculate the future value using the formula:
A = P(1 + i)^(nt)
A = 8000(1 + 0.015)^(4*1)
A ≈ $8,478.15
The amount of compound interest earned would be the difference between the future value and the principal amount:
Interest = A - P
Interest ≈ $8,478.15 - $8,000
Interest ≈ $478.15
Based on the above calculation, the correct amount of compound interest on $8,000 invested for one year at a 6% interest rate, compounded quarterly, is approximately $478.15.
The calculations you provided in your response seem incorrect. Please double-check your calculations using the steps outlined above.