5. brent opens two retirement accounts. he deposits $3,600 earning 5.5% compound interest annually for 3…

5. brent opens two retirement accounts. he deposits $3,600 earning 5.5% compound interest annually for 3 years, with no additional deposits or withdrawals. in the second account, brent makes monthly deposits of $300 for 3 years, as shown in the table below.\nbrents retirement account\n| year | deposit | new balance | interest earned (5.5%) | total balance |\n| ---- | ---- | ---- | ---- | ---- |\n| 1 | $3,600 | $3,600.00 | $201.30 | $3861.30 |\n| 2 | $3,600 | $7,461.30 | $410.37 | $7,871.67 |\n| 3 | $3,600 | $11,471.67 | $630.94 | \npart a: what is the total balance of brents retirement account in year 3 after making regular monthly deposits? enter your answer in the space provided.\npart b: how much more money is in the account where brent makes regular monthly deposits after 3 years than the account where he does not? enter your answer in the space provided.

5. brent opens two retirement accounts. he deposits $3,600 earning 5.5% compound interest annually for 3 years, with no additional deposits or withdrawals. in the second account, brent makes monthly deposits of $300 for 3 years, as shown in the table below.\nbrents retirement account\n| year | deposit | new balance | interest earned (5.5%) | total balance |\n| ---- | ---- | ---- | ---- | ---- |\n| 1 | $3,600 | $3,600.00 | $201.30 | $3861.30 |\n| 2 | $3,600 | $7,461.30 | $410.37 | $7,871.67 |\n| 3 | $3,600 | $11,471.67 | $630.94 | \npart a: what is the total balance of brents retirement account in year 3 after making regular monthly deposits? enter your answer in the space provided.\npart b: how much more money is in the account where brent makes regular monthly deposits after 3 years than the account where he does not? enter your answer in the space provided.

Answer

Explanation:

Step1: Calculate total monthly - deposits

There are 3 years and 12 months in a year, so the number of months is $3\times12 = 36$. The monthly deposit is $300$, so the total of monthly deposits is $300\times36=10800$.

Step2: Calculate the balance of the first account in year 3

From the table, the balance of the first account (with annual deposits) in year 3 is $11471.67 + 630.94=12102.61$.

Step3: Calculate the balance of the second account (month - ly deposits)

We need to use the future - value of an ordinary annuity formula $F = A\times\frac{(1 + r)^{n}-1}{r}$, where $A = 300$, $r=\frac{0.055}{12}$, and $n = 36$. First, calculate $(1+\frac{0.055}{12})^{36}\approx1.1709$. Then $\frac{(1+\frac{0.055}{12})^{36}-1}{\frac{0.055}{12}}\approx39.37$. So the future value of the annuity is $300\times39.37 = 11811$.

Step4: Answer Part A

The total balance of the account with monthly deposits is $11811$.

Step5: Answer Part B

The difference between the balance of the account with monthly deposits and the other account is $11811-12102.61=- 291.61$. This means the account with annual deposits has $291.61$ more.

Answer:

Part A: $11811$ Part B: $- 291.61$ (indicating the account with annual deposits has $291.61$ more)