Suppose that 2000 is loaned at a rate of 9% , compounded monthly. Assuming that no payments are made, find the amount owed after 4 years.
To find the amount owed after 4 years, we need to calculate the future value of the loan. The formula to calculate future value with monthly compounding is:
FV = P * (1 + r/n)^(n*t)
Where:
FV = Future Value
P = Principal amount (loan amount)
r = Annual interest rate (9%)
n = Number of times interest is compounded per year (monthly = 12)
t = Number of years (4)
Let's plug in the values and calculate the future value:
FV = 2000 * (1 + 0.09/12)^(12*4)
FV = 2000 * (1 + 0.0075)^(48)
FV = 2000 * (1.0075)^(48)
FV ≈ 2000 * (1.441740138)
FV ≈ 2883.48
So, the amount owed after 4 years is approximately $2883.48.
To find the amount owed after 4 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Amount owed after time t
P = Principal amount (initial loan)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case:
P = $2000
r = 9% = 0.09 (as a decimal)
n = 12 (compounded monthly)
t = 4 years
Plugging in these values into the formula, we have:
A = 2000(1 + 0.09/12)^(12*4)
Now, let's calculate the value:
A = 2000(1 + 0.0075)^(48)
A = 2000(1.0075)^(48)
A ≈ 2000(1.416403)
Calculating further:
A ≈ $2,832.81
Therefore, the amount owed after 4 years would be approximately $2,832.81.