question 11 of 40 at the beginning of year 1, paolo invests $500 at an annual compound interest rate of 4%…

question 11 of 40 at the beginning of year 1, paolo invests $500 at an annual compound interest rate of 4%. he makes no deposits to or withdrawals from the account. which explicit formula can be used to find the account’s balance at the beginning of year 5? what is the balance? a. $a(n)=500cdot(1 + 0.04)^n$; $608.33 b. $a(n)=500+(n - 1)(0.04cdot500)$; $580.00 c. $a(n)=500cdot(1 + 0.04)^{(n - 1)}$; $584.93 d. $a(n)=500+(0.004cdot500)^{(n - 1)}$; $516.00

question 11 of 40 at the beginning of year 1, paolo invests $500 at an annual compound interest rate of 4%. he makes no deposits to or withdrawals from the account. which explicit formula can be used to find the account’s balance at the beginning of year 5? what is the balance? a. $a(n)=500cdot(1 + 0.04)^n$; $608.33 b. $a(n)=500+(n - 1)(0.04cdot500)$; $580.00 c. $a(n)=500cdot(1 + 0.04)^{(n - 1)}$; $584.93 d. $a(n)=500+(0.004cdot500)^{(n - 1)}$; $516.00

Answer

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula for an initial investment $P$ with an annual interest rate $r$ compounded annually for $n$ years is $A(n)=P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $n$ is the number of years. Here, $P = 500$, $r=0.04$.

Step2: Determine the number of years

We want to find the balance at the beginning of year 5. Since the investment is made at the beginning of year 1, the number of years $n = 4$.

Step3: Calculate the balance

Substitute $P = 500$, $r = 0.04$, and $n = 4$ into the formula $A(n)=P(1 + r)^n$. So $A(4)=500\times(1 + 0.04)^4=500\times1.04^4=500\times1.16985856\approx584.93$. The explicit formula for the balance after $n$ years is $A(n)=500\times(1 + 0.04)^{n - 1}$ (because when $n = 1$, $A(1)=500$).

Answer:

C. $A(n)=500\times(1 + 0.04)^{(n - 1)}$; $$584.93$