Calculate the final amount of a 30-year mortgage loan of $120,000 with a compound interest rate of 4.25% compounded semiannually.
To determine the final amount of the mortgage loan, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (the initial loan amount)
r = the annual interest rate (expressed as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $120,000, the annual interest rate (r) is 4.25% (or 0.0425 as a decimal), the compounding occurs semiannually (n = 2), and the loan period is 30 years (t = 30).
Plugging in these values, the formula becomes:
A = $120,000(1 + 0.0425/2)^(2*30)
= $120,000(1 + 0.02125)^(60)
= $120,000(1.02125)^(60)
Calculating the exponent:
A = $120,000(2.20878817447)
= $264,954.58
Therefore, the final amount of the mortgage loan after 30 years would be approximately $264,954.58.