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.