Question

Determine the numerical value of the following factors using (a) linear interpolation, (b) the formula

1. (P/F,8.4%,15)

2. (A/F,17%,10)

Answer 1

1. (P/F,8.4%,15)

Here reference to tables does not provide a direct value to 8.4%. In such case we use the interpolation technique. We take two value for r = 8% and 9%, such that value between these at 8.4 is calculated.

At r = 8%.............. we have P/F value = 0.315242

At r = 8.4 ............... P/F value = X

At r = 9% ............ we have P/F value = 0.274538

(8.4 - 8) / (9 - 8 ) = (X - 0.315242 ) / (0.274538 - 0.315242)

0.4 = (X - 0.315242) / -0.040704

-0.0162816 = X - 0.315242

X = -0.0162816 + 0.315242 = 0.2990..............final answer

Using the formula method

P/F = 1 / (1.084)¹⁵= 0.2982....................final answer

Question - 2

A/F .......Annuity factors are generally tabulated for even values only. So we use interpolation technique to get A/F value ast 16% and 18% and derive the A/F value at 17%

At 16% ...................A/F Value = 0.0469

At 17 % ................. A/F value = X

At 18% .................. A/F Value = 0.0425

(17 - 16) / (18 - 16) = ( X - 0.0469) / ( 0.0425 - 0.0469)

( X - 0.0469)/ - 0.0044 = 1/2

( X - 0.0469) = - 0.0022

x = 0.0469 - 0.0022 = 0.0447...................Final answer

Direct formula ...... A/F = { [ (1+r)ⁿ - 1 ] / r }^-1 = { [ 1.17)¹⁰ - 1 ] / 0.10 } ^-1= 0.0447........final answer

Note A/F is nothing but the resiprocal of the FVA (Future value of annuity)