Suppose you borrow $4450 at 6.8% compounded semi-annually for 9 years.
How much do you owe after 9 years?
$
How much of that is interest?
$
To calculate the amount owed after 9 years, we'll use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (amount owed after 9 years)
P = Principal (initial borrowed amount) = $4450
r = Annual interest rate = 6.8% = 0.068
n = Number of times interest is compounded per year = 2 (semi-annually compounded)
t = Number of years = 9
Substituting these values into the formula, we get:
A = 4450(1 + 0.068/2)^(2*9)
A = 4450(1 + 0.034)^18
A ≈ 4450(1.034)^18
A ≈ 4450(1.785783)
A ≈ $7944.21
Therefore, you would owe approximately $7944.21 after 9 years.
To find the amount of interest, we subtract the principal from the final amount:
Interest = A - P
Interest = $7944.21 - $4450
Interest ≈ $3494.21
Therefore, approximately $3494.21 of that amount is interest.