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Rosa invests her tax return check into an account with a compounded interest rate of 1.75%. She plans on keeping the account open for 12 years. If she has $1600.87 in her account at the end of 12 years, approximately how much was her initial investment?

a) $1,300
b) $1,970
c) $7,690
d) $11,000

User Mgaughan
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1 Answer

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Final answer:

To determine Rosa's initial investment, the compound interest formula is re-arranged to solve for the principal amount. With the given parameters (12 years, 1.75% interest, and final amount of $1600.87), the initial investment is approximately $1,298.56, which is closest to option (a) $1,300.

Step-by-step explanation:

To determine Rosa's initial investment given the final amount in her account after 12 years with a compounded interest rate of 1.75%, we use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

  • A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money).
  • r is the annual interest rate (decimal).
  • n is the number of times that interest is compounded per year.
  • t is the time the money is invested for, in years.

As the question does not specify the frequency of compounding, we'll assume that the interest is compounded annually, so n = 1. We need to rearrange the formula to solve for P:

P = A / (1 + r)^t

Now we plug in the values given:

P = 1600.87 / (1 + 0.0175)^12

Calculating the above expression:

P ≈ 1600.87 / 1.232567

This gives us:

P ≈ $1,298.56

Therefore, the closest answer to Rosa's initial investment is option (a) $1,300.

User Moxn
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