If you borrow $1000 from the bank, and the effective annual rate is 9.4% with monthly compounding. How much do you pay after 2 years?
To calculate the amount you will pay after 2 years when borrowing $1000 from the bank with an effective annual rate of 9.4% and monthly compounding, we will need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan amount
P = the principal amount (initial loan amount)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $1000, the annual interest rate (r) is 9.4% (0.094 as a decimal), the number of times interest is compounded per year (n) is 12 (since it's monthly compounding), and the number of years (t) is 2.
Plugging in the values into the formula, we get:
A = $1000(1 + 0.094/12)^(12*2)
Calculating this:
A = $1000(1 + 0.00783)^(24)
A ≈ $1203.47
Therefore, you will pay approximately $1203.47 after 2 years when borrowing $1000 from the bank with an effective annual rate of 9.4% and monthly compounding.