Question

If $6000 is invested in an account earning 2.5% interest compounded continuously, how long will it take for the amount in the account to reach $10,000. (Assume no deposits or withdraws) Round to nearest tenth of a year.

Answer 1

To find out how long it will take for the amount in the account to reach $10,000, we can use the formula for continuous compounding interest: A = P*e(rt), where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years. In this case, it will take approximately 11.4 years for the amount in the account to reach $10,000.

Step-by-step explanation:

To find out how long it will take for the amount in the account to reach $10,000, we can use the formula for continuous compounding interest: A = P*e(rt), where A is the final amount, P is the principal amount (initial investment), r is the interest rate, and t is the time in years.

In this case, we have A = $10,000, P = $6000, and r = 2.5% (or 0.025 in decimal form). We need to solve for t.

Substituting the values into the formula, we get 10000 = 6000 * e(0.025t).

Divide both sides of the equation by 6000: 1.6667 = e(0.025t).

To isolate the exponent, take the natural logarithm (ln) of both sides of the equation: ln(1.6667) = 0.025t.

Divide both sides of the equation by 0.025: t = ln(1.6667)/0.025.

Using a calculator, we find that t ≈ 11.4 years.

Answer 2

6,000e^(.025t) = 10,000

e^(.025t) = 5/3

.025t = ln(5/3)

t = about 20.4 years