an initial deposit of $5,460.75 is placed in a simple interest savings account with an annual interest rate…

an initial deposit of $5,460.75 is placed in a simple interest savings account with an annual interest rate of 3.92%. after 51 months, the account balance is $6,370.51. part a: if the same initial deposit is invested for the same number of months at the same rate, with interest compounded semiannually, what is the final account balance? show all work. (3 points) part b: how does the compound interest account balance from part a compare to the simple interest final account balance of $6,370.51? (2 point)

an initial deposit of $5,460.75 is placed in a simple interest savings account with an annual interest rate of 3.92%. after 51 months, the account balance is $6,370.51. part a: if the same initial deposit is invested for the same number of months at the same rate, with interest compounded semiannually, what is the final account balance? show all work. (3 points) part b: how does the compound interest account balance from part a compare to the simple interest final account balance of $6,370.51? (2 point)

Answer

Explanation:

Step1: Convert months to years

The time $t$ in years for 51 months is $t=\frac{51}{12}= 4.25$ years. The annual interest rate $r = 3.92%=0.0392$, and the principal $P = 5460.75$. When compounded semiannually, $n = 2$.

Step2: Use the compound - interest formula

The compound - interest formula is $A=P(1 +\frac{r}{n})^{nt}$. Substitute the values: $A = 5460.75(1+\frac{0.0392}{2})^{2\times4.25}$. First, calculate the value inside the parentheses: $\frac{0.0392}{2}=0.0196$, and $1+\frac{0.0392}{2}=1.0196$. Then, calculate the exponent: $2\times4.25 = 8.5$. So, $A = 5460.75\times(1.0196)^{8.5}$. Calculate $(1.0196)^{8.5}\approx1.1777$. Then $A=5460.75\times1.1777\approx6430.07$.

Step3: Compare with simple - interest balance

The simple - interest final balance is $6370.51$. The compound - interest balance from part A ($6430.07$) is greater than the simple - interest balance. The difference is $6430.07 - 6370.51=59.56$.

Answer:

Part A: $$6430.07$ Part B: The compound - interest account balance of $$6430.07$ is greater than the simple - interest account balance of $$6370.51$ by $$59.56$.