Final answer:
Using the continuous compound interest formula, we convert the known end amount and interest rate to find the initial investment. The formula shows that the closest possible initial investment is $14,500. Therefore, the correct option is B.
Step-by-step explanation:
To calculate the initial investment amount with an ending balance of $16,343.15, an interest rate of 3 1/2% compounded continuously, and a time period of 6 years, we use the formula for continuous compounding interest: 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 before interest).
r is the annual interest rate (decimal).
t is the time the money is invested for, in years.
e is the base of the natural logarithm, approximately equal to 2.71828.
First, we convert the interest rate from a percentage to a decimal: 3 1/2% = 0.035. Our formula now looks like this:
A= Pe0.035t
We know that A=$16,343.15 and t=6, so we have:
$16,343.15 = Pe(0.035)(6)
To find the principal P, we divide both sides by e(0.035)(6):
P = $16,343.15 / e(0.035)(6)
A calculation with this formula gives us the value of P, which represents the initial investment. After performing the calculation, we find that the closest option is B. $14,500.