Force of Interest¶

It can be shown that as the compounding frequency approaches infinity, the nominal interest and discount rates approach a value $\delta$ called the force of interest:

$\lim_{m \to \infty} i^{(m)} = \lim_{m \to \infty} d^{(m)} = \delta.$

Examples¶

TmVal can handle force of interest problems by supplying a continually compounded interest rate to the Amount or Accumulation classes.

Suppose we have the force of interest $\delta = .05$ . What is the value at time 5 of 5,000 invested at time 0?

In [1]: from tmval import Amount, Rate

In [2]: my_amt = Amount(gr=Rate(delta=.05), k=5000)

In [3]: print(my_amt.val(5))
6420.1270834387105

Suppose instead, we have 5,000 at time 5. What is the present value if the force of interest remains at 5%?

In [4]: from tmval import Accumulation, Rate

In [5]: my_acc = Accumulation(gr=Rate(delta=.05))

In [6]: pv = my_acc.discount_func(t=5, fv=5000)

In [7]: print(pv)
3894.0039153570224

This could have also been solved by using the previously-introduced compound_solver():

In [8]: from tmval import compound_solver, Rate

In [9]: gr = Rate(delta=.05)

In [10]: pv = compound_solver(gr=gr, fv=5000, t=5)

In [11]: print(pv)
3894.0039153570224