To calculate how many years it will take for Mary's house loan premium to reach $898.90, we need to use the formula for compound interest:
A = P * (1 + r/100)^n
where A is the final amount, P is the initial amount (premium), r is the annual interest rate, and n is the number of years.
Substituting the given values:
$898.90 = $712 * (1 + 6/100)^n
Solving for n:
$898.90/$712 = (1 + 6/100)^n
Taking the natural logarithm of both sides:
ln($898.90/$712) = n * ln(1 + 6/100)
Dividing both sides by ln(1 + 6/100):
n = ln($898.90/$712) / ln(1 + 6/100)
Using a calculator to approximate the value, we get:
n = approximately 8.68 years
Therefore, it will take Mary approximately 8.68 years for her house loan premium to reach $898.90.