Question

Grace is going to invest $140 and leave it in an account for 13 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Grace to end up with $190?

Answer 1

The interest rate required for Grace to end up with $190 after 13 years of compound interest is approximately 10.3%.

Step-by-step explanation:

Compound interest is calculated using the formula:

A = P * e^(rt)

Where:

• A is the future amount (in this case, $190)
• P is the principal amount (in this case, $140)
• e is the mathematical constant approximately equal to 2.71828
• r is the interest rate (unknown)
• t is the time period in years (in this case, 13 years)

To determine the interest rate required, we can rearrange the formula:

r = ln(A/P)/(t)

Substituting the given values:

r = ln(190/140)/(13) = ln(1.357)/(13) = 0.103

Therefore, the interest rate required is approximately 0.103 or 10.3%.