$6350 is compounded semiannually at 14% for 12 years. What is the total amount in the compound interest account?
a = 6350 [1 + (.14 / 2)]^[12 / (1/2)]
To find the total amount in the compound interest account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = total amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $6350
r = 14% = 0.14 (as a decimal)
n = 2 (semiannually compounded, so 2 times per year)
t = 12 years
Now, let's substitute these values into the formula and calculate the total amount:
A = 6350(1 + 0.14/2)^(2*12)
A = 6350(1 + 0.07)^24
A = 6350(1.07)^24
A ≈ 6350(2.4713)
A ≈ $15,679.05
Therefore, the total amount in the compound interest account after 12 years would be approximately $15,679.05.
To calculate the total amount in the compound interest account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the principal amount (P) is $6350, the annual interest rate (r) is 14% or 0.14, the investment is compounded semiannually, so n = 2, and the investment period (t) is 12 years.
Substituting these values into the formula, we can calculate the total amount in the compound interest account:
A = 6350(1 + 0.14/2)^(2 * 12)
Let's calculate it step by step:
Step 1:
Divide the annual interest rate (0.14) by the number of times interest is compounded per year (2).
0.14/2 = 0.07
Step 2:
Add 1 to the result from step 1.
1 + 0.07 = 1.07
Step 3:
Multiply the result from step 2 by itself (as there are 2 compounding periods in a year) and raise it to the power of the number of years (12).
(1.07)^(2 * 12) = 1.07^24 ≈ 4.079
Step 4:
Multiply the result from step 3 by the principal amount (6350).
4.079 * 6350 ≈ 25911.35
Therefore, the total amount in the compound interest account is approximately $25,911.35.