A high school mathematics teacher puts $2000 into an annuity fund and then contributes $1800 per year into the fund for the next 30 years by making small weekly contributions. (We assume weekly contributions are close enough to continuous deposits so that we may use a differential equation model.) The fund grows at a rate of 7.5% per year.

(a) Write a differential equation that models the growth of this fund using $m(t)$ for the amount of money present in the fund.
(b) How much money will be in the fund after 30 years according to this model.

I feel confident that I can solve (b)

Question

A high school mathematics teacher puts $2000 into an annuity fund and then contributes $1800 per year into the fund for the next 30 years by making small weekly contributions. (We assume weekly contributions are close enough to continuous deposits so that we may use a differential equation model.) The fund grows at a rate of 7.5% per year.

(a) Write a differential equation that models the growth of this fund using $m(t)$ for the amount of money present in the fund.
(b) How much money will be in the fund after 30 years according to this model.

I feel confident that I can solve (b)