question 9 (4.5 points) you plan to deposit $76.850 into a savings account that has a 4.51% interest rate…

question 9 (4.5 points) you plan to deposit $76.850 into a savings account that has a 4.51% interest rate compounded monthly. what will be the balance of your savings account after 2 years? use this formula: $a = p(1+\frac{r}{n})^{nt}$ enter the dollar amount rounded to the nearest cent. your answer: question 10 (4.5 points) how much money should be deposited today in an account that earns 6.26% compounded monthly so that it will accumulate to $29,600 in 11 years? use this formula: $p=\frac{a}{(1 +\frac{r}{n})^{nt}}$ enter the dollar amount rounded up to the nearest cent. your answer: answer

question 9 (4.5 points) you plan to deposit $76.850 into a savings account that has a 4.51% interest rate compounded monthly. what will be the balance of your savings account after 2 years? use this formula: $a = p(1+\frac{r}{n})^{nt}$ enter the dollar amount rounded to the nearest cent. your answer: question 10 (4.5 points) how much money should be deposited today in an account that earns 6.26% compounded monthly so that it will accumulate to $29,600 in 11 years? use this formula: $p=\frac{a}{(1 +\frac{r}{n})^{nt}}$ enter the dollar amount rounded up to the nearest cent. your answer: answer

Answer

Explanation:

Step1: Identify the compound - interest formula variables for Question 9

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$. Given $P = 76.850$, $r=0.0451$ (since $4.51%=0.0451$), $n = 12$ (compounded monthly), and $t = 2$.

Step2: Substitute the values into the formula

$A=76.850(1 +\frac{0.0451}{12})^{12\times2}$. First, calculate the value inside the parentheses: $\frac{0.0451}{12}\approx0.00375833$, then $1+\frac{0.0451}{12}=1 + 0.00375833=1.00375833$. Next, calculate the exponent: $12\times2 = 24$. So, $A = 76.850\times(1.00375833)^{24}$. Using a calculator, $(1.00375833)^{24}\approx1.093797$. Then $A=76.850\times1.093797\approx84.07$.

Step3: Identify the compound - interest formula variables for Question 10

The compound - interest formula for present value is $P=\frac{A}{(1+\frac{r}{n})^{nt}}$. Given $A = 29600$, $r = 0.0626$ (since $6.26%=0.0626$), $n = 12$ (compounded monthly), and $t = 11$.

Step4: Substitute the values into the formula

First, calculate the value inside the parentheses: $\frac{0.0626}{12}\approx0.00521667$, then $1+\frac{0.0626}{12}=1 + 0.00521667 = 1.00521667$. Next, calculate the exponent: $nt=12\times11 = 132$. So, $(1+\frac{0.0626}{12})^{132}=(1.00521667)^{132}$. Using a calculator, $(1.00521667)^{132}\approx2.03777$. Then $P=\frac{29600}{2.03777}\approx14525.77$.

Answer:

Question 9: $84.07$ Question 10: $14525.77$