Question

The force of interest delta(t) is given by ln(1.5) for all non-negative t.

Find the accumulation function at 4, a(4).

	A.	5.0625
	B.	6.7420
	C.	5.2432
	D.	The correct answer does not appear here
	E.	4.0625

Answer 1

The realtionship between force of interest $\delta$ (k) and accumulation function a(t) is given by

a(t) = e
^s(s)ds

Let us assume that $\delta$ (t) is a constant function say, $\delta$ (t) = c, for all t where c is the constant.

a(t) = e
^cds

a(t) = e
^cds

Then, a(t) = e^ct since (
^{7 ds Jo
= s[t] - s[0] = t - 0 = t})

Solving we have $\delta$ (t) = ln(1.5) for all non negative 't'

This implies that a(t) = e^{[ln(1.5)]^t}

a(t) = 1.5^t

Solving for the given case where t = 4, we get a(t) = 5.0625

Option (A)

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