Final answer:
To calculate the value of Alice's investment in 2 years at a compounding interest rate of 16% quarterly, use the compound interest formula. The value of Alice's investment will be approximately $43,259.28.
Step-by-step explanation:
To calculate the value of Alice's investment in 2 years, we can use the formula for compound interest:
Final Amount = Principal Amount × (1 + Interest Rate/Number of Compounding Periods)^(Number of Compounding Periods × Number of Years)
Plugging in the given values:
Principal Amount = $31,600
Interest Rate = 16% = 0.16
Number of Compounding Periods = 4 (since it is compounded quarterly)
Number of Years = 2
Final Amount = $31,600 × (1 + 0.16/4)^(4 × 2)
Final Amount = $31,600 × (1 + 0.04)^8
Final Amount = $31,600 × 1.04^8
Final Amount = $31,600 × 1.3748
Final Amount = $43,259.28
Therefore, the value of Alice's investment in 2 years will be approximately $43,259.28 when rounded to the nearest cent.