We deposit $19000 into an account earning 3% interest compounded semiannually. How many years will it take for the account to grow to $47500 ? Round to 2 decimal places.
19000(1+.03/2)^(2n) = 47500
now just solve for n.
perhaps by taking a log to some base of both sides :)
To calculate the number of years it will take for the account to grow to $47,500, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future value (in this case, $47,500)
P is the principal amount (in this case, $19,000)
r is the annual interest rate (in this case, 3%, or 0.03)
n is the number of times that interest is compounded per year (in this case, semiannually, so n = 2)
t is the number of years
Rearranging the formula to solve for t:
t = log(A/P) / (n * log(1 + r/n))
Plugging in the given values:
t = log(47500/19000) / (2 * log(1 + 0.03/2))
Using a scientific calculator, we can evaluate this expression:
t ≈ log(2.5) / (2 * log(1.015))
t ≈ log(2.5) / (2 * 0.007177)
t ≈ log(2.5) / 0.014354
t ≈ 0.39794 / 0.014354
t ≈ 27.69
Rounding to two decimal places, it will take approximately 27.69 years for the account to grow to $47,500.