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We are given the following information
Investment = $5200
Annual interest rate = 4.2% = 0.042
Final amount = $16,500
Number of years = 27.7 years
Number of compoudings = quartely = 4
The student uses the following model
The general formula for compound interest is given by
As you can see, the number of compoundings is incorrect (3 vs 4)
The interest rate is also incorrect.
Let us substitute the given values into the above formula
Therefore, the final amount is approximately $16,543.5