To pay for a trip to visit his grandparents, Edward borrowed $1200 at an interest rate of 6.25% per year, compounded quarterly. How much must he repay if he pays the loan off at the end of one year?
To calculate how much Edward must repay at the end of one year, we need to consider the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount that must be repaid
P = the principal amount borrowed ($1200 in this case)
r = the annual interest rate (6.25% or 0.0625 as a decimal)
n = the number of compounding periods per year (4, since the interest is compounded quarterly)
t = the number of years (1 year in this case)
Now we can substitute these values into the formula and calculate the final amount:
A = 1200(1 + 0.0625/4)^(4*1)
A = 1200(1 + 0.015625)^4
A = 1200(1.015625)^4
A ≈ 1200(1.0625)
A ≈ 1275
Therefore, Edward must repay approximately $1275 at the end of one year.