A savings account with simple annual interest rate of 3.92% and an initial deposit of $5,460.75 yields a final account balance of $6,370.51 after 51 months.

Part A: Using the rate and term as the simple interest account, calculate the final account balance if the initial deposit is invested for the same number of months, with interest compounded semiannually. Show all work please.

Part B: Compare that simple interest final account balance with the compound interest final account balance.

B) It would be better to invest the principal in the compound interest account, as this account yields an additional $69.79 over the same period of the investment.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Part A

Given:

P = $5,460.75
r = 3.92% = 0.0392
n = 2 (semi-annually)
t = 51 months = 51/12 years = 4.25 years

Substitute the given values into the compound interest formula and solve for A:

[tex]\implies A=5460.75\left(1+\dfrac{0.0392}{2}\right)^{2 \times 4.25}[/tex]

[tex]\implies A=5460.75\left(1.0196\right)^{8.5}[/tex]

[tex]\implies A=5460.75\left(1.17937937...\right)[/tex]

[tex]\implies A=6440.2959...[/tex]

Therefore, the final amount is $6,440.30 (nearest cent).

Part B

Simple interest final account balance = $6,370.51

Compound interest final account balance = $6,440.30

The difference between the final account balances is:

[tex]\implies \$6440.30 - \$6370.51= \$69.79[/tex]

Therefore, it would be better to invest the principal in the compound interest account, as this account yields an additional $69.79 over the same period of the investment.