Assuming no deposits or withdrawals are made, the time it would take for the value of the account to reach $182,800 is 13.5 years.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:
B = P(1 + r/n)^t
where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded monthly, and t is the time in number of months
Based on the given information, t is the unknown and
B = $182,800
P = $75,000
r = 6.8% = 0.068
n = 1
Plug in the values and solve for the time it would take for the value to reach $182,800.
B = P(1 + r/n)^t
$182,800 = $75,000(1 + 0.068/1)^t
$182,800 = $75,000(1.068)^t
(1.068)^t = $182,800 / $75,000
(1.068)^t = 914/375
t = 13.5 years
Learn more about compound interest here: brainly.com/question/24924853
#SPJ4
