if $700 is deposited into an account with a 10.5% interest rate, compounded monthly, what is the balance…

if $700 is deposited into an account with a 10.5% interest rate, compounded monthly, what is the balance after 16 years?\nf = $?\nf = p(1 + \\frac{r}{n})^{nt}\nround to the nearest cent.

if $700 is deposited into an account with a 10.5% interest rate, compounded monthly, what is the balance after 16 years?\nf = $?\nf = p(1 + \\frac{r}{n})^{nt}\nround to the nearest cent.

Answer

Explanation:

Step1: Identify the values of P, r, n, and t

$P = 700$ (principal amount), $r=0.105$ (annual interest rate), $n = 12$ (compounding times per year), $t = 16$ (number of years).

Step2: Substitute values into the compound - interest formula

$F=P(1 +\frac{r}{n})^{nt}=700(1+\frac{0.105}{12})^{12\times16}$ First, calculate the value inside the parentheses: $\frac{0.105}{12}=0.00875$, then $1 + 0.00875=1.00875$. Next, calculate the exponent: $12\times16 = 192$. So, $F = 700\times(1.00875)^{192}$.

Step3: Calculate $(1.00875)^{192}$

Using a calculator, $(1.00875)^{192}\approx5.3377$.

Step4: Calculate the final amount F

$F=700\times5.3377 = 3736.39$.

Answer:

$3736.39$