Question

micaela is going to invest $46000 and leave it in an account for 16 years. assuming the interest is compounded continuously, what interest rate, to the nearest hundreth of a percent, would be required in order for micaela to end up with 73000?

Answer 1

Micaela would need an interest rate of approximately 3.9%, compounded continuously, to grow her investment from $46,000 to $73,000 in 16 years.

Step-by-step explanation:

To determine the interest rate required for Micaela's investment of $46,000 to grow to $73,000 in 16 years with compound interest being compounded continuously, we use the formula for continuous compounding A = Pert, where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (in decimal form).
• t is the time the money is invested or borrowed for, in years.
• e is the base of the natural logarithm.

Given:

• A = $73,000
• P = $46,000
• t = 16 years

We need to find r. Rearranging the formula to solve for r gives:

r = (1/t) * ln(A/P)

Calculating the value,

r = (1/16) * ln(73,000/46,000)

r ≈ 0.039 or 3.9% (to the nearest hundredth of a percent)

Micaela would need an interest rate of approximately 3.9% compounded continuously to reach her goal.