Final answer:
To find the original principal investment, the formula for compound interest is applied, and by plugging in the final amount, interest rate, number of compounding periods, and time, we can calculate Bob's principal investment.
Step-by-step explanation:
To calculate the original principal investment that Bob started with, the formula for compound interest needs to be used:
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.
In this case, we have A = $4132.85, r = 1% or 0.01, n = 4, and t = 4. The formula to find the principal P is:
$4132.85 = P(1 + 0.01/4)^(4*4)
By rearranging the formula to solve for P, we get:
P = $4132.85 / (1 + 0.01/4)^(4*4)
Calculating this gives us the original principal investment that Bob started with.