Question
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.
an account with a
compounded monthly, to have
your account 10 years later?
Ask by Mcguire Wheeler. in the United States
Jan 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
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.
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The Deep Dive
To solve for
in the equation
, we need to isolate
. Given that
,
,
(monthly compounding), and
:
-
Plug in the values:
-
Calculate
: -
Calculate
: -
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!