Question

Required information Problem 02.027 - Compound interest factors: Two ways to determine Consider the following factors. 1. (F/P,21%,34) 2. (A/G,17%,45) Problem 02.027.a - Linear interpolation of tabulated factors Find the numerical values of the factors using linear interpolation. The numerical value of factor 1 is . The numerical value of factor 2 is .

Answer 1

Factor 1 is (F/P,21%,34) = (1+0.21)³⁴ = 652.6834

Factor 2 is (A/G, 17%,45)

We can calculate the value through linear interpolation technique.

Here I don't have the values so I am assuming some values.

Consider a bond with

FV = $ 1000, coupon, C = $ 100, price, P = $ 850, N = 10 yrs

Let us assume interest rate is 15%

P = $100(P/A,15%,10) + $ 1000(P/F,15%,10)

P = 100* 5.018768 + 1000*0.247184

P = $ 501.87 + 247.18

P = $ 749.05

The price is $ 850 thus we have to decrease the interest rate. Let us assume rate = 12%

Price = 100(P/A,12%,10) + 1000(P/F,12%,10) = 565.02+ 321.97

Price = $ 886.99

Thus, the required rate lies in between 12 to 15 percent. We can solve using linear interpolation technique as follows

Rate = 12.80%

I have considered an example. To explain the linear interpolation method. Please contact if having any query thank you.