A bank account that accrues interest compounded continuously is modeled by the differential equation dA dt...

 

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A bank account that accrues interest compounded continuously is modeled by the differential equation dA dt <=TA where A is the amount of money in the account, r is the annual interest rate (in deci- mals) and t is time in years. Note that no withrawals are made and that the interest is automatically reinvested in the account. Problem 3 (12 pts.). A couple invests $5000 in an account that pays an annual interest rate of 4.5% compounded continuouly. i. Write down the differential equation that models how the principal grows over time. Include that initial condition. ii. Find a formula for the principal as a function of time. iii. How long is it before the account doubles in value? Problem 4 (12 pts.). The setting is the same as the preceding problem. Suppose that the couple, in addition to their initial investment, make payments into the account at a continuous rate of $30 per month. i. Write down the differential equation that models how the principal grows over time. Include that initial condition. ii. Find a formula for the principal as a function of time. iii. How long is it before the account doubles in value? 1 A bank account that accrues interest compounded continuously is modeled by the differential equation dA dt <=TA where A is the amount of money in the account, r is the annual interest rate (in deci- mals) and t is time in years. Note that no withrawals are made and that the interest is automatically reinvested in the account. Problem 3 (12 pts.). A couple invests $5000 in an account that pays an annual interest rate of 4.5% compounded continuouly. i. Write down the differential equation that models how the principal grows over time. Include that initial condition. ii. Find a formula for the principal as a function of time. iii. How long is it before the account doubles in value? Problem 4 (12 pts.). The setting is the same as the preceding problem. Suppose that the couple, in addition to their initial investment, make payments into the account at a continuous rate of $30 per month. i. Write down the differential equation that models how the principal grows over time. Include that initial condition. ii. Find a formula for the principal as a function of time. iii. How long is it before the account doubles in value? 1

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ANSWER PART The differential euqation will be modelled as dA dt dA A rA dA 4... View the full answer