find the accumulated value of an investment of $20,000 for 5 years at an interest rate of 1.15% if the money…

find the accumulated value of an investment of $20,000 for 5 years at an interest rate of 1.15% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously. click the icon to view some finance formulas. a. what is the accumulated value if the money is compounded semiannually? $ (round to the nearest cent as needed.) formulas in the provided formulas, a is the balance in the account after t years, p is the principal investment, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and y is the investments effective annual yield. a = p(1 + \\(\\frac{r}{n}\\))^nt p = \\(\\frac{a}{(1 + \\(\\frac{r}{n}\\))^nt}\\) a = pe^rt y=(1 + \\(\\frac{r}{n}\\))^n - 1

find the accumulated value of an investment of $20,000 for 5 years at an interest rate of 1.15% if the money is a. compounded semiannually; b. compounded quarterly; c. compounded monthly; d. compounded continuously. click the icon to view some finance formulas. a. what is the accumulated value if the money is compounded semiannually? $ (round to the nearest cent as needed.) formulas in the provided formulas, a is the balance in the account after t years, p is the principal investment, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and y is the investments effective annual yield. a = p(1 + \\(\\frac{r}{n}\\))^nt p = \\(\\frac{a}{(1 + \\(\\frac{r}{n}\\))^nt}\\) a = pe^rt y=(1 + \\(\\frac{r}{n}\\))^n - 1

Answer

Explanation:

Step1: Identify the values

The principal amount $P = 20000$, the annual interest rate $r=0.0115$ (since $1.15%= 0.0115$), the number of years $t = 5$, and when compounded semiannually, $n = 2$.

Step2: Use the compound - interest formula

The compound - interest formula is $A=P(1 +\frac{r}{n})^{nt}$. Substitute the values: $nt=2\times5 = 10$, $\frac{r}{n}=\frac{0.0115}{2}=0.00575$, and $1+\frac{r}{n}=1 + 0.00575=1.00575$. Then $A = 20000\times(1.00575)^{10}$.

Step3: Calculate $(1.00575)^{10}$

Using a calculator, $(1.00575)^{10}\approx1.05919$.

Step4: Calculate the final amount $A$

$A = 20000\times1.05919=21183.8$.

Answer:

$21183.80$