You have decided to purchase a new plasma TV. To do so , you must use your credit card to pay $1500 of the purchase price. The credit card company charges interest at a rate of 18.5% per year, compounded monthly. How much interest will you have to pay when you pay off the loan in one year?
To calculate the amount of interest you will have to pay when you pay off the loan in one year, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value of the loan (the amount you will owe after one year, including interest)
P is the principal amount (the initial loan amount)
r is the annual interest rate (18.5% in this case, expressed as a decimal 0.185)
n is the number of times the interest is compounded per year (12 times per year in this case, since it is compounded monthly)
t is the number of years (1 year in this case)
Let's plug in the values into the formula and solve for A:
P = $1500
r = 0.185
n = 12
t = 1
A = 1500(1 + 0.185/12)^(12*1)
A = 1500(1 + 0.015416666)^(12)
A = 1500(1.015416666)^(12)
A ≈ 1500(1.2016263)
A ≈ $1,802.44
Therefore, the future value of the loan after one year, including interest, will be approximately $1,802.44. To calculate the amount of interest, subtract the principal amount from the future value:
Interest = A - P
Interest = $1,802.44 - $1500
Interest = $302.44
So, you will have to pay approximately $302.44 in interest when you pay off the loan in one year.