If you borrow $25,500 for 18 months at the rate of 9% compounded monthly, how much must you repay at the end of the 18 months?
To calculate the total amount you need to repay at the end of 18 months, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Total amount to be repaid
P = Principal amount borrowed ($25,500)
r = Annual interest rate (9% or 0.09 as a decimal)
n = Number of times interest is compounded per year (monthly, so 12)
t = Time in years (18 months is equivalent to 1.5 years)
Let's substitute the values into the formula and calculate the repayment amount step by step:
First, divide the annual interest rate by the number of compounding periods per year to get the monthly interest rate:
monthly rate = r / n = 0.09 / 12 = 0.0075
Next, multiply the number of compounding periods per year by the time in years:
nt = 12 * 1.5 = 18
Now, plug the values into the compound interest formula and solve for A:
A = 25500(1 + 0.0075)^(18)
A = 25500(1.0075)^18
A ≈ 25500(1.148698434)
A ≈ $29,321.08
Therefore, you must repay approximately $29,321.08 at the end of the 18 months.
amount = 25500( 1 + .09/12)^18
= ...