how long will it take for a $6000 investment to grow to $9648 at an annual rate of 4.8% compounded monthly?

Question

Assume that no withdrawals are made. And do not round any intermediate computations, and round your answer to the nearest hundred.

Plz help I need this answer in an hour or quicker please!!!!!!!

Answer 1

Hello Jace,

The formula for compound interest is given by, A = P(1+r/n)^nt, where A is the future amount, P is the principal or current amount, r is the interest rate as a decimal, n is the number of compounding periods, and t is the number of years. So, we are given everything except t ( which is what we are solving for). Substituting the given values into the compound interest formula yields,

9648 = 6000(1+0.048/12)^12t, divide both sides by 6000 and simplify the base of the power

1.608 = (1.004)^12t , take the natural log of both sides and apply the log of a power property

ln(1.608) = 12t ln(1.004), divide both sides by 12ln(1.004)

t = ln(1.608) / 12ln(1.004)

t ≈ 9.915

Hence, it would take about 10 years for an investment of $6000 to grow to $9648 at an annual rate of 4.8% compounded monthly.