Answer:
Assuming a final balance of $3,000 for the second account, it would take 26,4 years of the first account to be exactly twice the balance in the second account.
Explanation:
First, we need to determine a quantity for the second account. We use the compound interest formula:
A = P(1 + i/n)^n*t
where:
A = Final value
P = initial value
i = interest rate
n = number of times the interest rate is compounded in the period
t = number of periods elapsed
We will assume that we need to find the number of years it takes for the second account to give a balance of $3,000. Under this sceneario, our values will be:
A = $3,000
P = $210
i = 11.2% annually
n = 1 (the interest rate is an efective annual rate, therefore, it is compounded once in a year)
t = x (the number of periods is the incognita)
Next, we plug the amounts into the equation and solve:
210 (1 + 0.112)^X = 3,000
(1.1112)^X = 3,000 / 210
(1.112)^X = 14.3
Remember that we use logarithms to solve for an unknown exponent
X * Log 1.112 = Log 14.3
X = Log 14.3 / Log 1.112
X = 25.0 years
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Now, we need to find how long it takes the second account to give a balance that doubles 3,000. (6,000)
1,250 (1 + 0.061)^X = 6,000
(1.061)^X = 4.8
X*log 1.061 = log 4.8
X = log 4.8 / log 1.061
X = 26.49 years
