Find total amount in the compound intrest account.
$2000 is compounded quarterly at a rate of 8% for 6 years. (Round to nearest Hundereths as needed)
amount = 2000(1.02)^24
= ...
so 48960?
How did you possibly get that ???
amount = 2000(1.02)^24
= 2000(1.608437)
= 3216.87
To find the total amount in a compound interest account, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = Total amount
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
Let's plug the given values into the formula:
Principal amount (P) = $2000
Annual interest rate (r) = 8% = 0.08 (as a decimal)
Number of times interest is compounded per year (n) = 4 (quarterly compounding)
Number of years (t) = 6
A = $2000(1 + 0.08/4)^(4*6)
Step 1: Simplify the rate per compounding period:
0.08/4 = 0.02
A = $2000(1 + 0.02)^(4*6)
Step 2: Calculate the exponent:
4*6 = 24
A = $2000(1.02)^24
Step 3: Raise 1.02 to the power of 24:
1.02^24 ≈ 1.593848
A = $2000(1.593848)
Step 4: Multiply the principal amount by the result:
A ≈ $3197.70
Therefore, the total amount in the compound interest account after 6 years would be approximately $3197.70.