Pregunta
Suppose you wish to retire at the age of 70 with
in savings. Determine your monthly payment into an IRA if the APR is
compounded monthly and you
begin making payments at 25 years old. Round your answer to the nearest cent, if necessary.
begin making payments at 25 years old. Round your answer to the nearest cent, if necessary.
Ask by Olson Medina. in the United States
Jan 24,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The monthly payment needed is approximately $33.90.
Solución
To determine the monthly payment into an IRA needed to accumulate
by the age of 70, we can use the future value of an annuity formula. The formula for the future value of an annuity is:
Where:
-
is the future value of the annuity (the amount you want to have at retirement, which is ). -
is the monthly payment (the value we want to find). -
is the monthly interest rate (annual interest rate divided by 12). -
is the total number of payments (number of years until retirement multiplied by 12).
Step 1: Identify the known values
- Future Value,
- Annual Interest Rate,
- Monthly Interest Rate,
- Current Age = 25
- Retirement Age = 70
- Total Years until Retirement =
- Total Payments,
Step 2: Calculate
and
Now, let’s calculate
and
:
Step 3: Substitute into the formula and solve for
Rearranging the future value formula to solve for
:
Now, let’s calculate
,
, and then
.
I’ll perform these calculations now.
Calculate the value by following steps:
Calculate the value by following steps:
-
step0: Calculate:
-
step1: Multiply the numbers:
Calculate or simplify the expression.
Calculate the value by following steps: -
step0: Calculate:
-
step1: Convert the expressions:
-
step2: Multiply by the reciprocal:
-
step3: Multiply the fractions:
-
step4: Multiply:
The calculations yield the following results: -
Monthly Interest Rate,
-
Total Payments,
Step 4: Substitute into the formula to find
Now we can substitute
,
, and
into the rearranged formula for
:
Let’s calculate
.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Remove the parentheses:
- step2: Add the numbers:
- step3: Convert the expressions:
- step4: Multiply the numbers:
- step5: Subtract the numbers:
- step6: Convert the expressions:
- step7: Multiply by the reciprocal:
- step8: Rewrite the expression:
- step9: Rewrite the expression:
- step10: Reduce the numbers:
- step11: Multiply:
The calculation gives us:
Conclusion
The monthly payment into the IRA needed to accumulate
by the age of 70, with an APR of
compounded monthly, is approximately $33.90.
Respondido por UpStudy AI y revisado por un tutor profesional
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Mind Expander
To achieve your goal of having $80,000 by the age of 70, we need to calculate how much you should contribute monthly starting at age 25 with an APR of 5.5% compounded monthly.
Using the future value of an ordinary annuity formula:
Where:
-
= future value ($80,000) -
= monthly payment (what we want to find) -
= monthly interest rate (5.5% / 12 months = 0.00458333) -
= total number of payments (45 years × 12 months = 540)
Rearranging the formula for
:
Now plug in the values:
Calculating
:
Now substituting back into the payment formula:
So, the monthly payment you need to make is approximately $87.76.

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