Pregunta
Paula has a client who wants to invest into an account that
earns
the account with an initial deposit of
an additional
Assuming no withdrawals or other deposits are made and
that the interest rate is fixed, the balance of the account
(rounded to the nearest dollar) after the eighth deposit is
a.)
b.)
c.)
d.)
(
earns
the account with an initial deposit of
an additional
Assuming no withdrawals or other deposits are made and
that the interest rate is fixed, the balance of the account
(rounded to the nearest dollar) after the eighth deposit is
a.)
b.)
c.)
d.)
(
Ask by Coleman Guzman. in the United States
Jan 26,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
After the eighth deposit, the account balance is $36,857.
Solución
To determine the balance of the account after the eighth deposit, we can use the Future Value of an Ordinary Annuity formula. Here’s a step-by-step breakdown:
Given:
- Initial Deposit (PMT): $4,000
- Interest Rate ®: 4% or 0.04 (annual)
- Number of Deposits (n): 8
Future Value Formula for an Ordinary Annuity:
Calculations:
-
Calculate
: -
Subtract 1:
-
Divide by the interest rate ®:
-
Multiply by the deposit amount (PMT):
-
Round to the nearest dollar:
Conclusion:
After the eighth deposit, the account balance (rounded to the nearest dollar) is $36,857.
Answer:
d.) $36,857
d.) $36,857
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Simplifique esta solución Mind Expander
To find the balance in the account after the eighth deposit, we can use the formula for the future value of a series of cash flows compounded annually. The formula for the future value of an annuity compounded annually is given by:
Where:
-
is the annual deposit ($4,000) -
is the annual interest rate (0.04) -
is the number of deposits (8) -
is the initial deposit ($4,000)
Substituting in the values, we have:
- Future Value of Annual Deposits:
- Future Value of the Initial Deposit:
Adding these amounts together gives us the total future value:
Now, since we are looking for the balance after the eighth deposit, we compute the total balance as:
- Final Calculation:
Total balance after eight deposits, using the previously found values equals approximately $42,331.
Based on your options:
None of the options given were close to $42,331.
None of the options given were close to $42,331.
However, please ensure the calculations are appropriately done or based on an understanding prior to it presented here.
To cycle back to the given options, consistency in categorization of financial growth is key to reaching the correct value based on initial conditions before the eighth contribution begins compounding. Thus revisions in foundational aspects of financial structuring could yield refined estimations.
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