what is the correct formula to use for the following problem:
Find compound amount for the deposit.Round to the nearest hundredth
$11000 at 6% compunded quarterly for 2years.
the one that i am thinking of is:
a = p(1 + (r)/(m))^mt
so my a = 1100;r=0.06;t=2
so the interest = r/m = 0.06/4 = 0.015
n= (t)(m)=n=(2)(4)=8
1100=p(1+0.015)^8
p= (1100)/((1.015)^8)
p= $976.48 this would be my answer
You have the compound formula correct, eight periods.
Your calculations are a mess. Why did you divide? You are looking for amount, not principal.
a = p(1 + (r)/(m))^mt.
The amount will have to be greater than the principal. Note the principal is 11 thousand, not hundred.
sorry i wrote it wrong it should read 1100 and at 6% compound quarterly for 2yrs.
so the from the formula i get
$1239.14 for the amount am i correct
No, your calculation is still incorrect. Let's go through the correct calculations step by step using the correct values:
Principal (p) = $11,000
Rate (r) = 6% = 0.06 (decimal form)
Time (t) = 2 years
First, we need to determine the number of compounding periods (n). Since it is compounded quarterly, we multiply the number of years by the number of compounding periods per year:
n = t * m = 2 * 4 = 8 (compounding quarterly for 2 years means 8 compounding periods)
Next, we can plug these values into the compound amount formula:
a = p(1 + (r/m))^(m*t)
a = 11000 * (1 + (0.06/4))^(4 * 2)
a = 11000 * (1 + 0.015)^8
Now, we can calculate the compound amount using a calculator or an online tool:
a ≈ $11,874.32
Therefore, the correct compound amount for the deposit of $11,000 at 6% compounded quarterly for 2 years is approximately $11,874.32 when rounded to the nearest hundredth.