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).\non olgas 16th birthday, her uncle invested $2,000 in an account that was locked into a 1.75% interest rate, compounded monthly. how much will olga have in the account when she turns 18? round to the nearest cent.

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).\non olgas 16th birthday, her uncle invested $2,000 in an account that was locked into a 1.75% interest rate, compounded monthly. how much will olga have in the account when she turns 18? round to the nearest cent.

Answer

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Convert the given values to the appropriate form

The principal amount $P=$2000$, the annual interest rate $r = 1.75%=0.0175$, the number of times compounded per year $n = 12$ (compounded monthly), and the time $t=18 - 16=2$ years.

Step3: Substitute the values into the formula

$A = 2000(1+\frac{0.0175}{12})^{12\times2}$. First, calculate the value inside the parentheses: $\frac{0.0175}{12}\approx0.00145833$, then $1+\frac{0.0175}{12}=1 + 0.00145833=1.00145833$. Next, calculate the exponent: $12\times2 = 24$. So, $A = 2000\times(1.00145833)^{24}$.

Step4: Calculate $(1.00145833)^{24}$

Using a calculator, $(1.00145833)^{24}\approx1.03557$.

Step5: Calculate the final amount $A$

$A = 2000\times1.03557=$2071.14$.

Answer:

$$2,071.14$