Question

Your bank account is sitting on $28,000. You started with a principal balance of $20,000. If the interest rate was 6% compounded continuously, how long was your money in the bank? Round to the nearest tenth.

A) 4.6 years
B) 5.6 years
C) 6.6 years
D) 7.6 years

Answer 1

To calculate the time it takes for your money to reach $28,000 with a continuous interest rate of 6%, we can use the continuous compounding formula. By substituting the given values and solving for time, we find that the money was in the bank for approximately 7.6 years.

Step-by-step explanation:

To calculate the amount of time it takes for your money to reach $28,000 with an interest rate of 6% compounded continuously, we can use the continuous compounding formula:

A = P * e^(rt)

Where:

• A is the final amount of money, which is $28,000
• P is the principal balance, which is $20,000
• e is the mathematical constant approximately equal to 2.71828
• r is the interest rate per year, which is 6% or 0.06 as a decimal
• t is the time in years that the money is left in the bank and needs to be calculated

Substituting the given values, we get:

$28,000 = $20,000 * e^(0.06t)

To solve for t, we can divide both sides of the equation by $20,000 and then take the natural logarithm of both sides:

ln($28,000/$20,000) = 0.06t

t = ln(1.4) / 0.06 ≈ 7.578 years

Rounding to the nearest tenth, the answer is D) 7.6 years.