I cannot figure this out for the life of me. Maybe I am overthinking it.

Question

Money is transferred into an account at the rate of R(t)=5000t(e^-0.6t)

If the account pays 2% interest compounded continuously, how much will accumulate in the account over a 9-year period?

Answer 1

Money at 2% grows like e^0.02t

The amount deposited at time t gets to grow for (9-t) years. Seems to me like the account balance after 9 years is thus

∫[0,9] R(t) * e^(.02(9-t)) dt

Answer 2

I may have misspoken. Take a look here for a discussion of the topic.

faculty.atu.edu/mfinan/2243/business65.pdf

Answer 3

actually, it appears I was right after all...