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Cameron invested $7,400 in an account paying an interest rate of 4\tfrac{3}{8}4 8 3 ​ % compounded continuously. Savannah invested $7,400 in an account paying an interest rate of 4\tfrac{3}{4}4 4 3 ​ % compounded daily. After 7 years, how much more money would Savannah have in her account than Cameron, to the nearest dollar?

User Lon Kaut
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Final answer:

To solve the problem, we calculate the future value of both investments using the continuous and daily compound interest formulas. After finding the total amount in each account after 7 years, we then determine the difference in value between the two accounts.

Step-by-step explanation:

The problem deals with compound interest and how it accrues differently when compounding continuously versus daily. To compare the final amounts in each account after 7 years, we use two different compound interest formulas.

For Cameron's investment with continuous compounding, we use the formula A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount, e is the base of the natural logarithm, r is the annual interest rate (as a decimal), and t is the time in years.

For Savannah's investment with daily compounding, we use the formula A = P(1 + r/n)nt, where n is the number of times interest is compounded per year. In this case, since the compounding is daily, n would be 365.

Once we have both final amounts, we subtract Cameron's total from Savannah's to find out how much more money Savannah would have in her account after 7 years.

User Ardaar
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