I know how to do simple interest on a loan but how would I figure compound interest on a loan $8,000 invested for one year at 6% compounded quarterly ? with rounded to the nearest dollar thanks in advance for explaining :)
I knew it was coming :)
you are going to do 6% a year compounded quarterly.
that means you will do 6%/4 each time
that is 1.5% every three months.
that means every three months you will multiply whatever is in the bank by 1.015
You do this four times in a year so you multiply the original amount by
1.015 *1.015*1.015*1.015
or 1.015^4
which is
1.06136
\So multiply that by 8,000
=8490.91
to the nearest dollar that is
8,491
so you made 491 in interest that year.
To calculate compound interest on a loan, you need to use the following formula:
A = P (1 + r/n)^(nt)
Where:
A is the final amount including interest
P is the principal amount (the initial investment)
r is the annual interest rate (as a decimal)
n is the number of times that interest is compounded per year
t is the number of years
In this case, you have an $8,000 investment for one year at a 6% interest rate compounded quarterly. Let's break it down step by step:
1. Convert the annual interest rate to a decimal: 6% = 0.06.
2. Determine the number of times that interest is compounded per year: In this case, it is compounded quarterly, which means four times per year (n = 4).
3. Plug the values into the formula:
A = 8000 (1 + 0.06/4)^(4*1)
4. Perform the calculations inside the parentheses:
A = 8000 (1 + 0.015)^(4)
5. Calculate the exponent:
A = 8000 (1.015)^(4)
6. Calculate the value inside the parentheses:
A = 8000 (1.06136)
7. Multiply the principal amount by the value inside the parentheses:
A ≈ 8000 * 1.06136 = 8490.88
8. Finally, round the result to the nearest dollar:
A ≈ $8,491
Therefore, the final amount, including compound interest, is approximately $8,491.