Mark borrowed $200 at 12% compound interest
for two years. If he makes no payments. How
much interest will he owe at the end of the second
year?
A $48.00
B $50.88
C $26.88
D $24.00***
200 (1.12)^2 = 250.88 total
- 200 principal = 50.88
To calculate the interest owed at the end of the second year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount including interest
P = the principal amount (in this case, the loan amount)
r = the annual interest rate (12% in this case)
n = the number of times that interest is compounded per year (usually 1 for annually)
t = the number of years the money is invested for (2 years in this case)
Plugging the values into the formula, we have:
A = 200(1 + 0.12/1)^(1*2)
A = 200(1 + 0.12)^2
A = 200(1.12)^2
A = 200(1.2544)
A = 250.88
To find the interest owed at the end of the second year, we subtract the principal amount (loan amount) from the final amount:
Interest = A - P
Interest = 250.88 - 200
Interest = 50.88
Therefore, the correct answer is B. Mark will owe $50.88 in interest at the end of the second year.
To find the amount of interest Mark will owe at the end of the second year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount including interest
P is the principal amount (the initial loan amount) = $200
r is the annual interest rate (written as a decimal) = 12% = 0.12
n is the number of times that interest is compounded per year = assuming it is compounded annually, n would be 1
t is the number of years = 2
Plugging in the values into the formula:
A = $200(1 + 0.12/1)^(1*2)
A = $200(1 + 0.12)^2
A = $200(1.12)^2
A = $200(1.2544)
A = $250.88
Now to find the amount of interest, we subtract the principal amount:
Interest = A - P
Interest = $250.88 - $200
Interest = $50.88
So, Mark will owe $50.88 in interest at the end of the second year.
Therefore, the correct answer is B: $50.88.