at the time of her grandsons birth, a grandmother deposits $11,000 in an account that pays 9% compounded…

at the time of her grandsons birth, a grandmother deposits $11,000 in an account that pays 9% compounded monthly. what will be the value of the account at the childs twenty - first birthday, assuming that no other deposits or withdrawals are made during this period? click the icon to view some finance formulas. the value of the account will be $□. (round to the nearest dollar as needed.)

at the time of her grandsons birth, a grandmother deposits $11,000 in an account that pays 9% compounded monthly. what will be the value of the account at the childs twenty - first birthday, assuming that no other deposits or withdrawals are made during this period? click the icon to view some finance formulas. the value of the account will be $□. (round to the nearest dollar as needed.)

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. Here, $P=$11000$, $r = 0.09$ (since $9%=0.09$), $n = 12$ (compounded monthly), and $t = 21$ years.

Step2: Substitute the values into the formula

$A=11000(1 +\frac{0.09}{12})^{12\times21}$ First, calculate the value inside the parentheses: $\frac{0.09}{12}=0.0075$, and $1 + 0.0075=1.0075$. Then, calculate the exponent: $12\times21 = 252$. So, $A = 11000\times(1.0075)^{252}$.

Step3: Calculate $(1.0075)^{252}$

Using a calculator, $(1.0075)^{252}\approx6.00917$.

Step4: Calculate the final amount $A$

$A=11000\times6.00917=$66090.87\approx$66091$

Answer:

$66091$