Tammy Smith Deposits $5000.00 in First Internets Bank 5-year CD which pays 5.22% interest compounded monthly how much interest will she have in the account in 5 years?
You used simple interest on a compound interest problem.
i = .0522/12 = .00435
n = 12(5) = 60
amount after 5 years
= 5000(1.00435)^60 = 6487.47
interest earned = 1487.47
I believe $1,305
I just did the math and that's what i got.
I got that also but its not correct and its driving me crazy
To calculate the amount of interest Tammy will have in her account after 5 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the total amount in the account after the specified time
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, Tammy deposits $5000.00 (P), the interest rate is 5.22% (5.22/100 = 0.0522) (r), the interest is compounded monthly (n = 12), and she plans to leave it in the account for 5 years (t).
Let's calculate the interest:
A = 5000(1 + 0.0522/12)^(12*5)
Now, let's evaluate this expression step by step:
Step 1: Calculate the value within parentheses (1 + 0.0522/12):
(1 + 0.0522/12) ≈ 1.00435
Step 2: Raise the value obtained in step 1 to the power of 60 (12 * 5):
(1.00435)^(60) ≈ 1.28138
Step 3: Multiply the result obtained in step 2 by the principal amount:
5000 * 1.28138 ≈ 6406.90
Therefore, after 5 years, Tammy will have approximately $6,406.90 in her account. The interest earned would be the difference between the total amount and her initial deposit:
Total Interest = $6,406.90 - $5,000.00 = $1,406.90
So, Tammy will have approximately $1,406.90 in interest in her account after 5 years.