Questions: Recently, More Money 4 U offered an annuity that pays 4.8% compounded monthly. If 982 is deposited into this annuity every month, how much is in the account after 4 years? How much of this is interest? Type the amount in the account: (Round to the nearest dollar.)

Recently, More Money 4 U offered an annuity that pays 4.8% compounded monthly. If 982 is deposited into this annuity every month, how much is in the account after 4 years? How much of this is interest? Type the amount in the account: (Round to the nearest dollar.)
Transcript text: Recently, More Money 4 U offered an annuity that pays $4.8 \%$ compounded monthly. If $\$ 982$ is deposited into this annuity every month, how much is in the account after 4 years? How much of this is interest? Type the amount in the account: $\$$ $\square$ (Round to the nearest dollar.)
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate Monthly Interest Rate and Total Months

The annual interest rate is \( 4.8\% \), which can be expressed as a decimal: \( 0.048 \). The monthly interest rate \( r \) is calculated as: \[ r = \frac{0.048}{12} = 0.004 \] The total number of months over 4 years is: \[ n = 4 \times 12 = 48 \]

Step 2: Calculate Future Value of the Annuity

Using the formula for the future value of an annuity: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] where \( P = 982 \), we find: \[ FV = 982 \times \frac{(1 + 0.004)^{48} - 1}{0.004} \approx 51851.2108 \] Rounding this to the nearest dollar gives: \[ FV \approx 51851 \]

Step 3: Calculate Total Deposits and Interest Earned

The total amount deposited over 4 years is: \[ \text{Total Deposits} = P \times n = 982 \times 48 = 47136 \] The interest earned is calculated as: \[ \text{Interest Earned} = FV - \text{Total Deposits} = 51851.2108 - 47136 \approx 4715.2108 \]

Final Answer

The amount in the account after 4 years is \( \boxed{51851} \) and the interest earned is approximately \( 4715.21 \).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Graph the equation using the slope and y-intercept. 2x + y = 1
failedAnswered
Name each compound and determine the charge an each ion in the compounds. Spelling counts. Li2O name of Li2O: Li charge O charge: CaS name of CaS: Ca charge: S charge
failedAnswered
The green line on the following graph shows the economy's long-term growth trend. Use the blue points (circle symbol) to plot the real GDP in each of the years listed. (Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.) Next, place the black point (plus symbol) on the graph to indicate the point on the real GDP curve that definitely represents a peak. Finally, place the grey point (star symbol) on the graph to indicate the point on the real GDP curve that definitely represents a trough. Calculate the percentage change in real GDP in each of the years shown. (Hint: The percentage change in real GDP equals the change in GDP from the previous year to the current year. For example, you can calculate the percentage change for 1981 by finding the change in GDP from 1980 to 1981, dividing this change by the level of GDP in 1980, and then multiplying the result by 100%.)
failedAnswered
If you have been exposed to a piece of information but it did not register with you, it would be said that the information was not properly - encoded. - retrieved. - systemized. - stored.
failedAnswered
1. When assessing a 12 year old diagnosed with autism spectrum disorder, what does the nurse expect? a. Hyperactivity and attention deficits b. Failure to have developed interpersonal skills c. History of disobedience and destructive acts d. High levels of anxiety when separated from a parent 2. A nurse assesses a 10 year old diagnosed with autism spectrum disorder. Which finding is most associated with the clients' disorder? a. The pattern of play is often restricted and repetitive b. Cries when separated from a parent c. Reads children's books outloud to others d. Occasional toileting accidents 3. A nurse refers a client with posttraumatic stress disorder to group therapy. Group therapy will likely be more beneficial than individual therapy for this client because group therapy may? a. Prevent reinforcement of the sense of self-blame b. Help alleviate anxiety and induce relaxation c. Help the client better express feelings d. Induce a sense of trust toward the staff 4. The psychiatric mental health nurse will perform the initial assessment of a client who has just been diagnosed with posttraumatic stress disorder. Which area would the nurse most likely address first?