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Which investment results in the greatest total amount?
Investment A: invested for 6 years compounded semiannually at .
Investment B: invested for 4 years compounded quarterly at .
Find the total amount of investment .
(Round to the nearest cent as needed.)

Ask by Fernandez Hill. in the United States
Jan 24,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The total amount for Investment A is $5,703.04.

Solution

To calculate the total amount for Investment A, we’ll use the compound interest formula:
Where:
  • (principal)
  • (annual interest rate)
  • (number of times interest is compounded per year, since it’s semiannually)
  • years (time)
Plugging in the values:
Calculating :
Now, multiply by the principal:
Total Amount for Investment A:

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Extra Insights

To find the total amount for Investment A compounded semiannually, we can use the formula for compound interest:
Where:
  • is the total amount after time ,
  • is the principal amount (the initial investment),
  • is the annual interest rate (in decimal),
  • is the number of times interest is compounded per year,
  • is the number of years the money is invested.
For Investment A:
  • (6% as a decimal)
  • (compounded semiannually)
Now, plug in the values:
Calculating :
So,
The total amount of Investment A is:

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