Questions: Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest ten dollars.) 400 deposited monthly for 20 years at 2% per year FV=

Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest ten dollars.) 400 deposited monthly for 20 years at 2% per year FV=
Transcript text: Find the amount accumulated $F V$ in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest ten dollars.) $\$ 400$ deposited monthly for 20 years at 2\% per year \[ F V=\$ \]
failed

Solution

failed
failed

Solution Steps

Step 1: Given Values

We are given the following values for the annuity:

  • Monthly deposit: \( P = 400 \)
  • Annual interest rate: \( r = 0.02 \)
  • Number of years: \( t = 20 \)
Step 2: Convert Annual Interest Rate to Monthly Interest Rate

To find the monthly interest rate, we divide the annual interest rate by 12: \[ r_{monthly} = \frac{r}{12} = \frac{0.02}{12} = 0.0016666666666666668 \]

Step 3: Calculate Total Number of Deposits

The total number of deposits over 20 years, with monthly deposits, is: \[ n = t \times 12 = 20 \times 12 = 240 \]

Step 4: Future Value of the Annuity

Using the future value of an annuity formula: \[ FV = P \times \left( \frac{(1 + r_{monthly})^n - 1}{r_{monthly}} \right) \] Substituting the values: \[ FV = 400 \times \left( \frac{(1 + 0.0016666666666666668)^{240} - 1}{0.0016666666666666668} \right) \] Calculating this gives: \[ FV \approx 117918.73374386992 \]

Step 5: Round the Future Value

Rounding the future value to the nearest ten dollars: \[ FV_{rounded} = 117920.0 \]

Final Answer

The amount accumulated in the annuity account is \\(\boxed{117920}\\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
17 Multiple Answer 1 point Select all that apply. Identify the modifier(s) in the sentences provided and select the sentences that do not contain errors with the modifier(s). Don bought a Great Dane from a neighbor that was too big for the doghouse. The Great Dane that Don bought from a neighbor was too big for the doghouse. Don bought a Great Dane that was too big for the doghouse from a neighbor. 18 Multiple Answer 1 point Select all that apply. Identify the modifier(s) in the sentences provided and select the sentences that do not contain errors with the modifier(s). After an hour's search, she found the money hidden under the rug. She found, after an hour's search, the money hidden under the rug. She found the money hidden under the rug after an hour's search. 19 Multiple Answer 1 point Select all that apply. Identify the modifier(s) in the sentences provided and select the sentences that do not contain errors with the modifier(s). Marinated in mustard sauce, the cook served a delicious ham. The cook served a delicious ham marinated in mustard sauce. The cook served a delicious ham that was marinated in mustard sauce.
failedAnswered
Determine cost of goods sold during the period under a periodic inventory system using the average-cost method. (Round ave cost per unit to 3 decimal places, e.g. 12.502 and final answer to 0 decimal places, e.g. 1,250.)
failedAnswered
The largest component of gross domestic income is A. wages. B. profits. C. rent. D. interest.
failedAnswered
Jonathan wants his company's culture to be more team-focused and less individual-focused. He sees that the company can improve communications, leadership, and group processes. On which target element is Jonathan focused? people organizational arrangements methods social factors
failedAnswered
Select all that apply Praising someone to others tends to have which of the following effects? It makes the complimented person upset. It provides colleagues with valuable information. It makes colleagues jealous of that person. It makes the complimented person grateful to you. It demonstrates your team spirit.