Question

Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?

Answer 1

it takes 8.8 years for the value of the account to reach $5,920.

Explanation:

We can use the formula A = P(1+r/n)^(nt) to find the time it takes for Ella's investment to reach $5,920.

A is the future value of the investment, P is the present value (initial investment), r is the interest rate, n is the number of compounding periods per year and t is the time in years.

Plugging in the given values:

5920 = 4900(1 + 0.03/12)^(12t)

To solve for t, we need to take the natural logarithm of both sides of the equation and divide by the logarithm of (1+0.03/12)

t = ln(5920/4900)/(12*ln(1+0.03/12))

t = approximately 8.8 years (to the nearest tenth of a year)

So it takes 8.8 years for the value of the account to reach $5,920.