Complete the table for a savings account in which interest is compounded continuously. (Round your answers to four decimal places.)
Initial Investment: $1,000
Annual % Rate: %
Time to Double: 15 yr
Amount After 9 Years:
2 = e^rt
ln 2 = r *15
r = 0.0462 or 4.62 %
A = 1000 * e^(0.0462 *9) =1515.72
To complete the table for a savings account with continuously compounded interest, you need the Annual % Rate and the Time to Double. Without these values, it is not possible to find the Amount After 9 Years.
To calculate the Amount After 9 Years, you can use the continuous compound interest formula:
A = P * e^(rt)
Where:
A = Amount after time t
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (in decimal form)
t = Time in years
However, since we don't have the annual interest rate, it is not possible to calculate the exact amount. Additionally, the Time to Double can provide an approximate estimate for the annual interest rate needed to double the initial investment in 15 years.
If you're given the Time to Double as 15 years, it means that the interest rate needed to double the investment in that time is the annual interest rate (r) for which A = 2 * P. In this case, P = $1,000.
To find r, we can use the formula:
A = P * e^(rt)
2 * P = P * e^(r * 15)
2 = e^(r * 15)
Taking the natural logarithm (ln) of both sides:
ln(2) = r * 15
Now, solve for r:
r = ln(2) / 15
Once you have the annual interest rate, you can calculate the Amount After 9 Years using the continuous compound interest formula mentioned earlier:
A = P * e^(rt)
However, please note that without the specific annual interest rate, it is not possible to provide an exact amount after 9 years.