the equation, $a = p(1+\frac{0.03}{4})^{4t}$, represents the amount of money earned on a compound interest…

the equation, $a = p(1+\frac{0.03}{4})^{4t}$, represents the amount of money earned on a compound interest savings account with an annual interest rate of 3% compounded quarterly. determine the value of $p$ if after 7 years, the account balance is $10,478.05. round the answer to the nearest hundredths place.\n$p = 1,383.08$\n$p = 4,579.77$\n$p = 8,500.00$\n$p = 10,170.34$

the equation, $a = p(1+\frac{0.03}{4})^{4t}$, represents the amount of money earned on a compound interest savings account with an annual interest rate of 3% compounded quarterly. determine the value of $p$ if after 7 years, the account balance is $10,478.05. round the answer to the nearest hundredths place.\n$p = 1,383.08$\n$p = 4,579.77$\n$p = 8,500.00$\n$p = 10,170.34$

Answer

Explanation:

Step1: Identify the values of variables

We have $A = 10478.05$, $r=0.03$, $n = 4$ (compounded quarterly), and $t = 7$. The compound - interest formula is $A=P(1+\frac{r}{n})^{nt}$.

Step2: Substitute values into the formula

Substitute the known values into the formula: $10478.05=P(1 +\frac{0.03}{4})^{4\times7}$. First, calculate $(1+\frac{0.03}{4})^{4\times7}$. $(1+\frac{0.03}{4})^{4\times7}=(1 + 0.0075)^{28}$. Using a calculator, $(1 + 0.0075)^{28}\approx1.232712$.

Step3: Solve for $P$

We have the equation $10478.05=P\times1.232712$. To find $P$, divide both sides of the equation by $1.232712$. $P=\frac{10478.05}{1.232712}\approx8500.00$.

Answer:

C. $P = 8,500.00$