Suppose you borrow $500 and you plan to pay it back all at once in 5 years. You are charged 2% interest compounded monthly.
What is the total amount you will need to pay when the loan is due?
Round your answer to the nearest dollar.
$1100?
Good grief NO, that is not even a reasonable guess!
i = .02/12 = .0016666.. (don't round, keep in your calculator)
n = 5(12) = 60
amount = 500(1.0016666..)^60 = .....
so... what is it?
Oh nvm- its $553
k thanks bye ~
To calculate the total amount you will need to pay when the loan is due, we need to consider the principal (the borrowed amount) and the interest.
First, let's calculate the monthly interest rate. Divide the annual interest rate by the number of compounding periods in a year. In this case, since the interest is compounded monthly, there are 12 compounding periods in a year. So the monthly interest rate is 2% / 12 = 0.02 / 12 = 0.00167 or 0.167%.
Next, we can use the compound interest formula to calculate the future value of the loan. The formula is:
A = P(1 + r/n)^(nt)
Where:
A is the future value or total amount
P is the principal (the borrowed amount)
r is the interest rate per compounding period (in decimal form)
n is the number of compounding periods per year
t is the number of years
Plugging in the values:
P = $500
r = 0.00167
n = 12
t = 5
A = 500(1 + 0.00167/12)^(12*5)
Now, let's calculate this using a calculator or a spreadsheet:
A ≈ $579.43 (rounded to the nearest cent)
Therefore, the total amount you will need to pay when the loan is due is approximately $579.43. However, you mentioned rounding the answer to the nearest dollar, so the rounded total amount is $579.