Answer:
10 years, 3 months
Step-by-step explanation:
To answer this, use the compound amount formula:
A = P(1+r/n)^(nt), where r is the annual interest rate as a decimal fraction, n is the number of compounding periods, and P is the initial amount. t represents the number of years.
Using the given info, we write $10,000 = $4,000(1 + 0.09/12)^(12*t) and set out to find the value of t, which represents the number of years necessary for the initial $4,000 to reach the end amount $10,000.
Let's solve 10000 = 4000(1 + 0.09/12)^(12 t) for t, as follows:
Divide both sides of this equation by 4000, to obtain an equation for (1 + 0.09/12)^(12 t):
2.5 = (1 + 0.09/12)^(12 t)
Simplifying the quantity inside the first set of parentheses, we get
2.5 = (1+ 0.0075)^(12*t), or 2.5 = 1.0075^(12*t)
Taking the log of both sides will eliminate the exponent (12*t):
log 2.5 = 12*t*log 1.0075. Solve this for t by dividing both sides of this equation by 12*log 1.0075:
log 2.5 * t 0.39794
-------------------- = ---------------------- = 10.2191 = t
12*log 1.0075 12*(0.003245)
$4,000 left in this account paying 9% with monthly compounding will increase to $10,000 after 10.22 years (10 years, 3 months)
