Confusion about Kellison 1.4

The problem is:

Quote:

It is known that a(t) is of the form at^2 + b. If 100 invested at 0 accumulates to 172 at t = 3, find the accumulated value at t = 10 of 100 invested at t = 5.

I know I have to solve for a and b:



a(0) = 1 = b

100a(3) = 172

which implies that a(3) = 1.72 and a = 0.08



Now I need to figure out the value of the investment. My approach was to use the "time value": 100 dollars invested at t = 5 is the same as some amount k invested at t = 0:



ka(5) = 100

k = 100 / a(5)

k = 100/3



So, the value of the investment should be



k (a(10) - a(5)), which comes to 200.



I'm looking at a solutions manual, and it says the value is 300. The solution solves for a and b (their solution agrees with mine) and then "just says" the answer is



100 * a(10)/a(5) = 300



I really don't understand where this is coming from. It looks like Kellison and the solutions manual author just assumed the interest regime was compounding. But it's not. It has a polynomial accumulation function.

Confusion about Kellison 1.4