Question

possible answers are 3.5， 1.99， 3， 2.43， 2.89

33. You are given the amount function, A(t)=10 (1.06)“t, where t is the number of years. Let i(4)be the nominal interest rate compounded quarterly, d (12) be the nominal discount rate compounded monthly and & be the annual constant force of interest Calculate 10 (4)+20d (12)+308

Answer 1

Solution:

10*i(4) + 20*d(12) + 30*$\delta$

Put the value of i(4), d(12) & $\delta$ from working note 3 , 4 & 5 respectively

=10*0.015 + 20* 0.005 + 30*0.06

=2.05

Working Notes:

Amount funtion given in the question is

A(t) = 10*(1.06)^t, where t is the number of years. ...................1

this is the equation of Future value compounded annually as given in question that t is number of years.

Equation of FV compounded annually is

FV = PV(1+i)^n .......................2

, where i is nominal interest rate for the year & n is years

On comparing 1 & 2

10*(1+.06)^t = PV(1+i)^n

We get i = 0.06 (i.e. nominal interest rate for the year)

Calculation of i(4) i.e. nominal interest rate compounded quarterly

i(4) = i/4

i(4) = .06/4

i(4) = .015 ...............................3

Calculation of d(12) i.e. nominal discount rate compounded monthly

d(12) = i/12

d(12) = .06/12

d(12) = .005 ................................4

Calculation of $\delta$ i.e. annual constant force of interest

$\delta$ = i

$\delta$ = .06 ..................................5