Hak Young is tired at the end of the semester and decides he really needs a break so he pays for a one week all-inclusive trip to Disney Land with his credit card. In total the trip cost $3000 and his credit card charges 21% interest compounded monthly. He doesn’t expect that he will have the money to pay off his credit card until he graduates and is working full time which will be at least another 18 months. How much will Hak Young’s trip have truly cost him by the time he can start to pay it off? What will be the total interest paid?
To calculate the total cost of Hak Young's trip and the total interest paid, we need to calculate the compound interest over the 18-month period.
The formula to calculate compound interest is given by:
A = P(1 + r/n)^(nt)
Where:
A = the final amount including interest
P = the principal amount (the initial cost of the trip)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Let's calculate the total cost:
Principal amount (P) = $3000
Annual interest rate (r) = 21% = 0.21 (converted to decimal form)
Number of times compounded per year (n) = 12 (monthly compounding)
Number of years (t) = 18 months / 12 months/year = 1.5 years
Plugging the values into the formula:
A = 3000(1 + 0.21/12)^(12*1.5)
A = 3000(1 + 0.0175)^(18)
A ≈ 3000(1.0175)^18
A ≈ 3000(1.347734168)
A ≈ $4043.20
Therefore, the trip will truly cost Hak Young approximately $4043.20 when he starts to pay it off.
To calculate the total interest paid, we can subtract the principal amount from the final amount:
Total interest paid = A - P
Total interest paid = $4043.20 - $3000
Total interest paid ≈ $1043.20
Therefore, Hak Young will end up paying approximately $1043.20 in interest for his Disney Land trip.
To calculate the total cost of the trip and the total interest paid, we need to determine the future value of the $3000 trip after 18 months with the 21% interest rate compounded monthly.
Step 1: Calculate the monthly interest rate
To find the monthly interest rate, divide the annual interest rate by 12:
Monthly interest rate = 21% / 12 = 0.0175
Step 2: Calculate the number of compounding periods
Since the interest is compounded monthly for 18 months, the number of compounding periods is 18:
Number of compounding periods = 18
Step 3: Calculate the future value of the trip
Using the formula for compound interest:
Future Value = Principal * (1 + Monthly interest rate)^Number of compounding periods
Future Value = $3000 * (1 + 0.0175)^18
Step 4: Calculate the total cost of the trip
The total cost of the trip includes the initial cost and the interest accrued:
Total cost = Principal + Interest
Total cost = $3000 + Future Value
Step 5: Calculate the total interest paid
The total interest paid is the difference between the total cost and the initial cost:
Total interest paid = Total cost - Principal
Now let's calculate the values in the following steps:
Step 1:
Monthly interest rate = 0.0175
Step 2:
Number of compounding periods = 18
Step 3:
Future Value = $3000 * (1 + 0.0175)^18
Step 4:
Total cost = $3000 + Future Value
Step 5:
Total interest paid = Total cost - $3000
Let's calculate the values in the next step.
So is debt is increasing at a monthly rate of .21/12 for 18 months
= 3000(1 + .21/12)^18 = ....
Your turn to finish it