I'm helping my little sister in her math homework. I just got stuck in this problem. Can anyone please help us out. I'm guessing it's letter C. Am I correct?
A small company borrows $50,000 at 11% compounded monthly. The loan is due in 4 years. How much interest will the company pay? Round to the nearest cent.
A)$26,776.12
B)$27,175.47
C)$27,479.90
D)$77,479.9
How did you make a guess for your sister?
Did she work it out, in which case there should be details of the work.
You won't be helping her if you gave her the right answer without telling her why or how.
Can she post her answer?
well I came up with because I just guessed it that's why i'm here to ask for help becuase I just can't come up with the actual answer. I come up with 22,000
50,000x.11=5500
5500/4=22,000
what am I doing wrong here?
Every month the principal is increased by (.11/12)principal
or
principal = original principal [1 +(.11/12)]^48 because 4 years is 48 months
so
principal after 48 months = 50,000[1.091666667]^48
=77479.90
and
77479.90-50000 = 27479.90
To calculate the interest that the company will pay, we can use the formula for compound interest:
A = P(1 + r/n)^(nt) - P
Where:
A = the total amount (including principal and interest)
P = the principal amount (the initial loan amount)
r = the annual interest rate (as a decimal)
n = the number of times compounded per year
t = the number of years
In this problem:
P = $50,000
r = 11% = 0.11 (as a decimal)
n = 12 (compounded monthly)
t = 4 years
Using this information, we can plug it into the formula and calculate the total amount:
A = 50000(1 + 0.11/12)^(12*4) - 50000
Calculating this expression will give us the total amount the company will owe, including principal and interest. Subtracting the principal will give us the amount of interest paid.
To find the correct option, calculate and compare the interest paid for each option. In this case, let's calculate the interest for option C and see if it matches:
Interest for C = A - P = $27,479.90 - $50,000 = -$22,520.10
As we can see, the interest calculated for option C is negative, which means it is incorrect. Therefore, option C is not the correct answer.
Now, you can continue the same process to calculate the interest for the other options (A, B, and D) and compare the results to find the correct answer.