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Rashon is going to invest in an account paying an interest rate of compounded quarterly. How much would
Rashon need to invest, to the nearest dollar, for the value of the account to reach in 13 years?

Ask by Craig Cruz. in the United States
Jan 23,2025

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Rashon needs to invest $8,301 initially to reach $20,200 in 13 years.

Solución

To determine how much Rashon needs to invest initially to reach $20,200 in 13 years with an interest rate of 6.9% compounded quarterly, we can use the compound interest formula:
Where:
  • = Future Value ($20,200)
  • = Present Value (initial investment)
  • = Annual interest rate (6.9% or 0.069)
  • = Number of compounding periods per year (4 for quarterly)
  • = Number of years (13)
Step-by-Step Calculation:
  1. Identify the known values:
  2. Rearrange the formula to solve for :
  3. Calculate the growth factor:
  4. Compute the present value ( ):
  5. Round to the nearest dollar:
Conclusion:
Rashon needs to invest $8,301 initially to have an account value of $20,200 in 13 years with the given interest rate and compounding frequency.
Answer:
Rashon should invest $8,301 initially to reach a $20,200 account value in 13 years.

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Mind Expander

To determine how much Rashon needs to invest today, we can use the formula for compound interest:
Where:
  • is the amount of money accumulated after n years, including interest.
  • is the principal amount (the initial amount of money).
  • is the annual interest rate (decimal).
  • is the number of times that interest is compounded per year.
  • is the number of years the money is invested or borrowed.
Given:
  • (which is )
  • (quarterly)
We need to solve for :
Calculating the values inside the parentheses:
Now calculating the exponent:
So we can rewrite the equation:
Calculating :
Now substituting back to find :
Now, solving for :
Therefore, Rashon needs to invest approximately dollars, rounded to the nearest dollar.
So, Rashon should invest about $8,786 today to reach his goal!
Planting some financial seeds can pay off big in the future! Did you know that compounding interest works almost like a snowball effect? The more time your money has to grow, the larger it gets as interest adds up not just on your initial investment but on the interest already earned.
If you’re looking for something fun and a bit of a brain workout, check out some online compound interest calculators! They’re super handy for visualizing how different rates, times, and compounding frequencies can impact your investment. You might be surprised at what a difference a few extra years or a slightly different interest rate makes!

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