Final answer:
The amount to be paid back on an $800 loan after three months with a 15% monthly compound interest is approximately $1216.70, calculated using the compound interest formula adjusted for monthly compounding.
Step-by-step explanation:
To calculate the amount you would have to pay back on an $800 loan with a 15% monthly compound interest rate after three months, you can use the formula for compound interest: A = P(1 + r/n)^(nt), where:
- A is the future value of the loan, including interest.
- P is the principal amount (the initial amount of the loan).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for, in years.
Since the interest rate is compounded monthly, we have:
- P = $800
- r = 15% per month, or 0.15
- n = 12 (compounded monthly)
- t = 3/12 year (since 3 months is a quarter of a year)
However, in this scenario, because the interest rate is given per month and we want the amount after 3 months, we adjust our formula to work directly with monthly compounding. Thus, we use:
- n = 1 (compounded monthly)
- t = 3 (months)
Let's calculate the amount:
A = 800(1 + 0.15/1)^(1*3)
A = 800(1 + 0.15)^3
A = 800(1.15)^3
A = 800(1.520875)
A ≈ $1216.70
Therefore, after 3 months, you would have to pay approximately $1216.70 to the money lender.