Suppose that a loan of $6500 is given at an interest rate of 7% compounded each year. Assume that no payments are made on the loan. Follow the instructions below. Do not do any rounding.
Find the amount owed at the end of 2 years.
To find the amount owed at the end of 2 years, we need to calculate the compound interest for each year and add it to the initial loan amount.
First, we calculate the interest earned in the first year using the formula for compound interest:
Interest1 = Principal * (1 + Interest Rate)^Time - Principal
= $6500 * (1 + 0.07)^1 - $6500
= $6500 * 1.07 - $6500
= $6500 * 0.07
= $455
So, the interest earned in the first year is $455.
Next, we find the interest earned in the second year:
Interest2 = Principal * (1 + Interest Rate)^Time - Principal
= $6500 * (1 + 0.07)^2 - $6500
= $6500 * 1.07^2 - $6500
= $6500 * 1.1449 - $6500
= $6500 * 0.1449
= $941.85
Thus, the interest earned in the second year is approximately $941.85.
Finally, we add the interest earned in both years to the initial loan amount to find the total amount owed:
Amount Owed = Principal + Interest1 + Interest2
= $6500 + $455 + $941.85
= $6500 + $455 + $941.85
≈ $7896.85
Therefore, the amount owed at the end of 2 years is approximately $7896.85.
To find the amount owed at the end of 2 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the loan
P = the initial principal (the 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:
P = $6500
r = 7% = 0.07 (as a decimal)
n = 1 (compounded annually)
t = 2 years
Plugging in the values into the formula:
A = 6500(1 + 0.07/1)^(1*2)
A = 6500(1 + 0.07)^2
A = 6500(1.07)^2
A = 6500(1.1449)
A ≈ $7446.85
Therefore, the amount owed at the end of 2 years is approximately $7446.85.