Question

If $ 4000 is invested in a bank account at an interest rate of 10 per cent per year, compounded continuously, then how many years will it take for your balance to reach $ 20000 ? round to 2 decimal places.

Answer 1

To find the number of years it will take for a balance to reach $20,000 when $4,000 is invested at an interest rate of 10% per year compounded continuously, we can use the formula for continuous compound interest. Using this formula, it will take approximately 6.93 years for the balance to reach $20,000.

Step-by-step explanation:

To find the number of years it will take for a balance to reach $20,000 when $4,000 is invested at an interest rate of 10% per year compounded continuously, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:

• A is the final amount
• P is the principal amount (initial investment)
• e is the base of the natural logarithm (approximately 2.71828)
• r is the interest rate per year
• t is the time in years

Substituting the given values into the formula, we have:

20000 = 4000 * e^(0.1t)

To solve for t, we can divide both sides of the equation by 4000:

5 = e^(0.1t)

Next, take the natural logarithm of both sides of the equation:

ln(5) = ln(e^(0.1t))

Since ln(e^(0.1t)) simplifies to 0.1t, we have:

ln(5) = 0.1t

Finally, divide both sides of the equation by 0.1:

t = ln(5) / 0.1

Using a calculator, we find that t is approximately 6.93 years, rounded to 2 decimal places.