an initial investment amount p, an annual interest rate r, and a time t are given. find the future - value…

an initial investment amount p, an annual interest rate r, and a time t are given. find the future - value of the investment when interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. then find (e) the doubling - time t for the given interest rate.\np = $115,000, r = 3.2%, t = 6 yr\n\na) the future value of the investment when interest is compounded annually is $138923.60.\n(type an integer or a decimal. round to the nearest cent as needed.)\n\nb) the future value of the investment when interest is compounded monthly is $139306.51.\n(type an integer or a decimal. round to the nearest cent as needed.)\n\nc) the future value of the investment when interest is compounded daily is $139340.84.\n(type an integer or a decimal. round to the nearest cent as needed.)\n\nd) the future value of the investment when interest is compounded continuously is $139342.11.\n(type an integer or a decimal. round to the nearest cent as needed.)\n\ne) find the doubling - time for the given interest rate.\nt=\n(type an integer or decimal rounded to two decimal places as needed.)

an initial investment amount p, an annual interest rate r, and a time t are given. find the future - value of the investment when interest is compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. then find (e) the doubling - time t for the given interest rate.\np = $115,000, r = 3.2%, t = 6 yr\n\na) the future value of the investment when interest is compounded annually is $138923.60.\n(type an integer or a decimal. round to the nearest cent as needed.)\n\nb) the future value of the investment when interest is compounded monthly is $139306.51.\n(type an integer or a decimal. round to the nearest cent as needed.)\n\nc) the future value of the investment when interest is compounded daily is $139340.84.\n(type an integer or a decimal. round to the nearest cent as needed.)\n\nd) the future value of the investment when interest is compounded continuously is $139342.11.\n(type an integer or a decimal. round to the nearest cent as needed.)\n\ne) find the doubling - time for the given interest rate.\nt=\n(type an integer or decimal rounded to two decimal places as needed.)

Answer

Explanation:

Step1: Recall continuous - compounding doubling - time formula

The formula for continuous - compounding doubling - time $T$ when the interest rate is $r$ (in decimal form) is $T=\frac{\ln(2)}{r}$. Given $r = 3.2%=0.032$.

Step2: Calculate the doubling - time

Substitute $r = 0.032$ into the formula $T=\frac{\ln(2)}{r}$. We know that $\ln(2)\approx0.693147$. So $T=\frac{0.693147}{0.032}\approx21.66$.

Answer:

$21.66$