The force of interest $\delta$(t) is 10% p.a. at the start of the year, 7% p.a. at the end of 9th month and 5% p.a. at the end of the year. $\delta$(t) is linear during the two periods before and after the end of 9th month.
In such scenario, how do I calculate the accumulated value at the end of the year, of a sum invested at the start of the year?
Basucally, how to account for a linear change in the force of interest?
I tried interpolation but it doesn't match the answer. Is there some other way?