Final answer:
To determine how much more money Vani would have in her account than Piper after 16 years, we apply the formulas for continuously compounded interest and daily compounded interest, respectively. Then, we calculate the difference between the two amounts.
Step-by-step explanation:
The student is asking about the future value of investments made by Piper and Vani, with different compound interest rates and compounding frequencies. To find out how much more money Vani would have in her account than Piper after 16 years, we need to apply the formula for continuously compounded interest for Piper's investment, and the formula for daily compounded interest for Vani's investment.
For continuously compounded interest, the formula is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), e is Euler's number (approximately 2.71828), and t is the time in years. For daily compounding, the formula is A = P(1 + r/n)nt, where n is the number of times that interest is compounded per unit t.
Using Piper's rate of 9, 3/8 % (or 0.09375 in decimal form) and Vani's rate of 9, 3/4 % (or 0.0975 in decimal form), with both investing $710, we calculate the future values after 16 years for each. We then subtract Piper's future value from Vani's to find the difference in dollars, rounded to the nearest dollar.