note: please make sure to properly format your answers. all dollar figures in the answers need to include…

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).\narianna deposits $500 in an account that pays 1.3% interest, compounded semi - annually. how much is in the account at the end of two years?

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).\narianna deposits $500 in an account that pays 1.3% interest, compounded semi - annually. how much is in the account at the end of two years?

Answer

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is (A = P(1+\frac{r}{n})^{nt}), where (P) is the principal amount, (r) is the annual interest rate (in decimal form), (n) is the number of times interest is compounded per year, and (t) is the number of years. Given (P=$500), (r = 1.3%=0.013), (n = 2) (semi - annual compounding), and (t = 2) years.

Step2: Substitute the values into the formula

Substitute the values into the formula: [ \begin{align*} A&=500(1 +\frac{0.013}{2})^{2\times2}\ &=500(1+0.0065)^{4}\ \end{align*} ] First, calculate (1 + 0.0065=1.0065). Then ((1.0065)^{4}\approx1.0263) (using a calculator: (1.0065\times1.0065\times1.0065\times1.0065)).

Step3: Calculate the final amount

Multiply (P) by the result of ((1+\frac{r}{n})^{nt}): (A = 500\times1.0263=$513.15)

Answer:

($513.15)