A110 Force the Interest Pt 2

Question 1

before you shortcut the accumlation function from the force of interest, what must to check first?

Answer 1

make sure that a(0) is actually 1. If it’s not divide the denominator by what a(0) is.

Question 2

what if the force of interest is multiplied by a constant, k?

Answer 2

δ_t = [a(t)]^k

Question 3

Suppose an account has a constant force of interest δ. Express the effective annual interest rate i in terms of δ.

Answer 3

i = e^δ - 1

Question 4

Suppse an account has a constant effective anual interest rate of i. Express the force of interest δ_t in terms of i.

Answer 4

δ_t = δ = ln(1+i)

Note: When δ_t is constant, we drop the subscript and simply write it as δ.

Question 5

how to we accumlate and discount if the force of interest is constant for compound interest?

Answer 5

a(t_1,t_2) = e^δ(t_2-t_1)

a^-1(t_1,t_2) = e^-δ(t_2-t_1)

Question 6

how to we accumlate for simple interest using the force of interest?

Answer 6

principal * a(t_1, t_2) = principal a(t_2)/a(t_1)