5. elena deposits $5,600.00 into a cd that pays 4.3% interest, compounded semi - annually.\na. how much…

5. elena deposits $5,600.00 into a cd that pays 4.3% interest, compounded semi - annually.\na. how much interest does the account earn in the first 6 months?\np = 5600 r = 0.0215 t = 0.5\n5600×0.0215 = 5600×\\frac{215}{10000}=\\frac{5600×215}{10000}\nb. what is the balance at the end of the first 6 months?\nc. how much interest does the account earn in the second 6 months?\nd. what is the balance at the end of the year?\ne. how much interest did the account earn overall?\nf. how much interest would the same account earn in one year if it is compounded annually?\ng. how much more interest does elena earn when her account is compounded semi - annually vs. compounded annually?

5. elena deposits $5,600.00 into a cd that pays 4.3% interest, compounded semi - annually.\na. how much interest does the account earn in the first 6 months?\np = 5600 r = 0.0215 t = 0.5\n5600×0.0215 = 5600×\\frac{215}{10000}=\\frac{5600×215}{10000}\nb. what is the balance at the end of the first 6 months?\nc. how much interest does the account earn in the second 6 months?\nd. what is the balance at the end of the year?\ne. how much interest did the account earn overall?\nf. how much interest would the same account earn in one year if it is compounded annually?\ng. how much more interest does elena earn when her account is compounded semi - annually vs. compounded annually?

Answer

Explanation:

Step1: Calculate first - 6 - month interest

The annual interest rate is $4.3%=0.043$. Since it's compounded semi - annually, the interest rate per 6 - month period $r = \frac{0.043}{2}=0.0215$, and the principal $P = 5600$. Using the simple - interest formula $I=Pr$, we have $I_1=5600\times0.0215 = 119.4$.

Step2: Calculate balance at end of first 6 months

The balance $A_1$ at the end of the first 6 months is the sum of the principal and the first 6 - month interest. So $A_1=5600 + 119.4=5719.4$.

Step3: Calculate second 6 - month interest

The principal for the second 6 - month period is $A_1 = 5719.4$. Using the simple - interest formula again with $r = 0.0215$, we get $I_2=5719.4\times0.0215\approx122.97$.

Step4: Calculate balance at end of the year

The balance $A_2$ at the end of the year is $A_2=5719.4+122.97 = 5842.37$.

Step5: Calculate overall interest

The overall interest $I_{total}=A_2 - 5600=5842.37 - 5600 = 242.37$.

Step6: Calculate interest with annual compounding

If compounded annually, using the formula $A = P(1 + r)^t$ with $P = 5600$, $r=0.043$, and $t = 1$, we have $A_{annual}=5600\times(1 + 0.043)=5600\times1.043 = 5840.8$. The interest $I_{annual}=5840.8 - 5600=240.8$.

Step7: Calculate the difference in interest

The difference in interest $\Delta I=242.37 - 240.8 = 1.57$.

Answer:

a. $119.4$ b. $5719.4$ c. $\approx122.97$ d. $5842.37$ e. $242.37$ f. $240.8$ g. $1.57$