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 = $115000, r = 3.2%, t = 6 yr\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.)\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.)\nc) the future value of the investment when interest is compounded daily is $\n(type an integer or a decimal. round to the nearest cent 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 = $115000, r = 3.2%, t = 6 yr\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.)\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.)\nc) the future value of the investment when interest is compounded daily is $\n(type an integer or a decimal. round to the nearest cent as needed.)

Answer

Explanation:

Step1: Recall compound - interest formula for daily compounding

The formula for compound interest when compounded $n$ times a year is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $n$ is the number of times compounded per year, and $t$ is the number of years. For daily compounding, $n = 365$. Given $P=$115000$, $r = 0.032$, and $t = 6$.

Step2: Substitute values into the formula

$A=115000(1 +\frac{0.032}{365})^{365\times6}$. First, calculate the value inside the parentheses: $\frac{0.032}{365}\approx0.0000876712$, then $1+\frac{0.032}{365}=1 + 0.0000876712=1.0000876712$. Next, calculate the exponent: $365\times6 = 2190$. Then, $(1.0000876712)^{2190}\approx1.21977$. Finally, $A = 115000\times1.21977=$139273.55$.

Answer:

$139273.55$