Answer:
10.6
Explanation:
To find out how long the person must leave the money in the bank until it reaches $22,600, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (22600 dollars in this case)
P = the principal amount (9500 dollars)
r = the annual interest rate (5.75% expressed as 0.0575)
n = the number of times the interest is compounded per year (in this case, annually, so n = 1)
t = the time in years
Substituting the given values into the formula, we have:
22600 = 9500(1 + 0.0575/1)^(1*t)
Simplifying:
2.3789 = (1.0575)^t
To solve for t, we take the logarithm of both sides:
log(2.3789) = log((1.0575)^t)
Using logarithm properties, we can bring the exponent down:
log(2.3789) = t * log(1.0575)
Now, we can solve for t by dividing both sides of the equation:
t = log(2.3789) / log(1.0575)
Using a calculator, we find:
t ≈ 10.6
Therefore, the person must leave the money in the bank for approximately 10.6 years to reach $22,600.