find the effectivee rate correspoding to 3% compounded quarterly
The formula for effective rate I found is (1+ i/n)^n - 1
where i is the annual rate as a decimal and n is the number of periods.
Here i=.03 so the effective rate is and n is 4 since there are 4 compounding periods.
(1+ .03/4)^4 - 1 = something you can do. If you want it as a percentage, multiply the number by 100 an use the % symbol.
BTW, are you the person who asked this question on Sunday?
"you have deposited 1000 dollars in your savings account with n annual interest rate of 4 percent compounded monthly. how much money are you going to have in your account after six months?"
"well theres another part of it if you could help me with.
"in the same problem find the effective interest rate after six months? "
You wanted the effective interest rate when i=.04 and the compounding was every 6 mos.
I only ask because I had to repost that one.
To find the effective rate corresponding to 3% compounded quarterly, you can use the formula (1 + i/n)^n - 1, where i is the annual interest rate as a decimal and n is the number of compounding periods.
In this case, i = 0.03 (3% as a decimal) and n = 4 (since it is compounded quarterly).
First, calculate (1 + i/n)^n:
(1 + 0.03/4)^4 = (1.0075)^4 ≈ 1.0304.
Next, subtract 1 and multiply by 100 to express it as a percentage:
1.0304 - 1 = 0.0304.
0.0304 * 100 = 3.04%.
Therefore, the effective rate corresponding to 3% compounded quarterly is approximately 3.04%.
Regarding your additional question, if the annual interest rate is 4% compounded monthly and you want to find the amount after six months, you would use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A is the final amount
P is the initial principal (1000 dollars in this case)
r is the annual interest rate as a decimal (0.04 in this case)
n is the number of compounding periods per year (12 in this case since it's compounded monthly)
t is the time in years (6/12 = 0.5 years in this case)
Plugging in these values, the calculation would be:
A = 1000 * (1 + 0.04/12)^(12*0.5)
A ≈ 1000 * (1.0033)^(6)
A ≈ 1000 * 1.02020
A ≈ 1020.20
Therefore, after six months, you would have approximately $1020.20 in your savings account.
If you have any further questions, feel free to ask!