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Project 1 Jerry is helping his elderly mother to organize her financial investments. One of her investment funds started 7 years ago, with the initial deposit unknown. The interest rate did not change. (1) Draw a possible graph of the balance A against time t (years) since the fund started. Explain any interesting feature of the graph. (2) Jerry found that 2 years after the fund was set up, the balance was $60,000 and was increasing at the (instantaneous) rate of $2,400 per year. Using this information, plus what you know about the shape of the A graph, estimate the balance of the fund at t = 8. (3) Using all the data given so far, derive a function Alt). You may use a continuous compounding model. Explain to Jerry why such a model works, even though the interest may not be compounded continuously, (4) Use the function obtained in part (3) to check how accurate the estimate in part (2) is. (5) Use the function obtained in part (3) to find how long will it take from now for the fund to reach the balance of $100,000. Project 1 Jerry is helping his elderly mother to organize her financial investments. One of her investment funds started 7 years ago, with the initial deposit unknown. The interest rate did not change. (1) Draw a possible graph of the balance A against time t (years) since the fund started. Explain any interesting feature of the graph. (2) Jerry found that 2 years after the fund was set up, the balance was $60,000 and was increasing at the (instantaneous) rate of $2,400 per year. Using this information, plus what you know about the shape of the A graph, estimate the balance of the fund at t = 8. (3) Using all the data given so far, derive a function Alt). You may use a continuous compounding model. Explain to Jerry why such a model works, even though the interest may not be compounded continuously, (4) Use the function obtained in part (3) to check how accurate the estimate in part (2) is. (5) Use the function obtained in part (3) to find how long will it take from now for the fund to reach the balance of $100,000

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