1. A 3,500.00 principal earns 3% interest, compounded semi annually. After 20 years, what is the balance in the account
A. 7,700.00
B. 4,713.99
C. 5,600.00
D. 6,349.06
Steve, I got the second one. It was 18,112.45. But I still cannot get the first one.
yeah
Well, it seems like you're having quite a thrilling time with these calculations! Math can sometimes be a bit puzzling, but don't worry, I'm here to help.
To solve this problem, we can use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
Where:
A = the balance after time t
P = the principal amount
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years
Now let's plug in the values given in the problem:
P = $3,500.00
r = 0.03 (3% as a decimal)
n = 2 (compounded semiannually)
t = 20
A = 3500(1 + 0.03/2)^(2*20)
Calculating that mess (believe me, I'm not a big fan of math either), we get:
A = $6,349.06
So, the correct answer is option D. Congratulations on reaching the grand finale of your math quest! Now go out and celebrate with some laughter – you deserve it!
To calculate the balance in the account after 20 years with a $3,500.00 principal earning 3% interest compounded semi-annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future balance
P = the principal amount
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 $3,500.00, the annual interest rate (r) is 3% or 0.03, the number of times interest is compounded per year (n) is 2 (semi-annually), and the number of years (t) is 20.
Substituting these values into the formula, we have:
A = 3,500.00(1 + 0.03/2)^(2*20)
Simplifying this expression, we get:
A = 3,500.00(1 + 0.015)^(40)
= 3,500.00(1.015)^(40)
Using a calculator, we calculate (1.015)^(40) to be approximately 2.208.
Thus,
A ≈ 3,500.00 * 2.208 ≈ $7,728.00
Therefore, the balance in the account after 20 years would be approximately $7,728.00.
Since this answer is not one of the options given, it appears there may be an error. Double-check your calculations or verify if any other information has been provided.
To calculate the balance in an account with compound interest, we can use the formula:
A = P * (1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial investment)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, the principal (P) is $3,500.00, the annual interest rate (r) is 3% or 0.03 as a decimal, interest is compounded semiannually (n = 2), and the time period (t) is 20 years.
Using the given values, we can solve for A:
A = $3,500.00 * (1 + 0.03/2)^(2*20)
First, divide the annual interest rate by the number of times interest is compounded per year:
A = $3,500.00 * (1 + 0.015)^(2*20)
Next, multiply the exponent (2*20) to get:
A = $3,500.00 * (1.015)^40
Now, find the value of (1.015)^40 using a calculator or spreadsheet:
A ≈ $3,500.00 * 1.787140
A ≈ $6,254.99
The balance in the account after 20 years is approximately $6,254.99.
Now, let's check the options provided:
A. 7,700.00 - This is not the correct answer.
B. 4,713.99 - This is not the correct answer.
C. 5,600.00 - This is not the correct answer.
D. 6,349.06 - This is not the correct answer.
Therefore, none of the given options match the calculated balance.