John Roe, an employee of the Gap, loans $3000 to another employee at the store. He will be repaid at the end of 4 years with interest at 6% compounded quartly. How much will John be repaid?
3000(1+.06/4)^(4*4) = 3806.96
To calculate the amount John will be repaid, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount after time t
P = the principal amount (initial loan)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
Given that P = $3000, r = 6% = 0.06, n = 4 (compounded quarterly), and t = 4 years, we can substitute these values into the formula:
A = 3000(1 + 0.06/4)^(4*4)
A = 3000(1 + 0.015)^16
A = 3000(1.015)^16
Now let's calculate the value of (1.015)^16:
(1.015)^16 ≈ 1.2674
Substituting this back into the equation:
A ≈ 3000 * 1.2674
A ≈ $3,802.20
Therefore, John will be repaid approximately $3,802.20 at the end of 4 years.
To calculate the amount that John will be repaid after 4 years with interest compounded quarterly, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
A = the final amount that will be repaid
P = the principal amount (the initial loan amount), which is $3000
r = the annual interest rate, which is 6% (written as a decimal, 0.06)
n = the number of compounding periods per year, which is 4 (since interest is compounded quarterly)
t = the number of years, which is 4
Plugging in these values into the formula, we get:
A = 3000 * (1 + 0.06/4)^(4*4)
Let's calculate this:
A = 3000 * (1 + 0.015)^(16)
A = 3000 * (1.015)^(16)
A ≈ 3000 * 1.2762801
So, John will be repaid approximately $3,828.84 at the end of 4 years.