Payments are made at a rate of t+5 dollars.
What do you mean by payments being "made at a rate of"? Are you saying that "t + 5 dollars are deposited at" some sort of time-interval or frequency? If so, for what interval or frequency does "t" stand? If not, what do you mean?
Interest is credited at a force of interest 1/(5+t).
What do you mean by interest being credited "at a force of interest"? Do you mean that interest payments are added to the account at a certain rate of interest (that is, in terms of a certain percentage of the principal)? If not, what do you mean? Either way, what sort of interest is it? Simple? Compound? If compound, how often? Annually? Daily? Something else?
What is the accumulated value at the end of 10 years?
I found the effective rate of interest at t=10 to be 11.6%
So, at some point in the tenth year (at the beginning? at the end? at some other point?), a payment is made (by whom?) (into the original account?) in the amount of $15. The interest rate (for only the day of the deposit? for the entire year preceding? for the entire year afterwards?) was, according to the formula provided, given by 1/15 = 0.0666... = 6.666...% = \(\displaystyle \, 6\dfrac{2}{3}\%\, \) interest. How did you arrive at 11.6%?
I used the formula \(\displaystyle \,F(v)\, =\, \int_0^n \, R(t)\, a(n\,-\,t)\,dt\)
And got 17.4 which is a bit too low
What is "R(t)"? For what do "a", "n", and "t" stand? If the integral is a function in terms of "v", why is there no "v" within the integral expression? What values or expressions did you plug into the variables? Why? What were your steps? How did you arrive at your answer?
Note: Unless there are fees which subtract from the account, the minimum amount (assume a once-yearly deposit with zero interest ever) in the account at the end of ten years would be:
. . . . .\(\displaystyle \displaystyle \sum_{t\, =\, 1}^{10}\, (t\, +\, 5)\, =\, \sum_{t\, =\, 1}^{10}\, t\, +\, 10\,\cdot\, 5\, =\, \dfrac{10\, \cdot\, 11}{2}\, +\, 50\, =\, 55\, +\, 50\, =\, 105\)
This suggests that something is massively wrong with your process. So please reply with a clear statement of the exercise and a complete listing of your reasoning and steps. Thank you!
