Pregunta
upstudy study bank question image url

How much would you have to deposit in
an account with a interest rate,
compounded monthly, to have in
your account 10 years later?
Round to the nearest cent.

Ask by Mcguire Wheeler. in the United States
Jan 21,2025

Solución de inteligencia artificial de Upstudy

Respuesta verificada por el tutor

Responder

You need to deposit $547.36 today to have $1,100 in your account after 10 years with a 7% annual interest rate compounded monthly.

Solución

To determine how much you need to deposit today ( ) to have $1,100 in your account after 10 years with a 7% annual interest rate compounded monthly, we can use the future value formula for compound interest:
Where:
  • (future value)
  • (annual interest rate)
  • (number of times interest is compounded per year)
  • (number of years)
Step 1: Solve for
Rearrange the formula to solve for :
Step 2: Plug in the values
Step 3: Calculate the denominator
Step 4: Compute
Final Answer:

Respondido por UpStudy AI y revisado por un tutor profesional

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The Deep Dive

To solve for in the equation , we need to isolate . Given that , , (monthly compounding), and :
  1. Plug in the values:
  2. Calculate :
  3. Calculate :
  4. Now, calculate :
So, the amount to deposit is approximately:

Imagine you’re planning a sunny vacation or a new gadget splurge in a decade! Knowing the historical power of compound interest is like having a financial wand—thanks to this magic, your money can grow even while you’re dreaming of that trip or product! It’s the reason why savings accounts with higher interest rates can be a great ally, pushing you just a little closer to your goals over time.
As for real-world trends, many folks underestimate the power of starting early—even a small deposit can blossom brilliantly over ten years! Think about your interests—what’s something fun you’d splurge on in the future? Maybe a travel spree or a tech upgrade? Start saving today, and watch your dreams unfold thanks to that savvy little interest compounding every month!

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