this is 3.5 and 3.6 Evaluate, using (3.5) and the tabular values of (A/P, i%, n)

Question

this is 3.5 and 3.6

Evaluate, using (3.5) and the tabular values of (A/P, i%, n) given in Appendix A (AF, 15%,8), (c)(A/F,12% , 40). , (a) (AIRS:20, (b) 3.16 Ans. (a)0.03358; (b) 0.0T285; (c)0.00130 3.17 Estimate the following factors, using (3.6), and compare with the correct values as given by (2.6: (a) (A/P,8%,80), (b)(A/P, 4%. 120). (c) (AIP, 19.08%, 100). Ans. (a) 0.08 (correct value, 0.0802): (b) 0.0475 (correct value, 0.0477): (b) 0.1908 (correct value, 0.1908) 30 ALGEBRAIC RELATIONSHIPS AND SOLUTION PROCEDURES [CHAP. 3 From the interest tables in Appendix A, determine the value of each of the following compound interest factors using linear interpolation. Compare each value with the exact answer obtained from the appropriate formula in Chapter 2. (a) (FP7,5%, 12), (b) (FP, 12% , 47), (c) (PF, 51%,20), (d) (FIA, 4%, 38), (e) (FIA, 48%. 38). (f) (AlF,11 6,30), (g) (A/P,5%, 57), (h) (A/P.71%,57), (i) 3.18 (PlA, 10 %, 30), (J ) (A/G, 81%. I 5), (k) (A/G, 131%, 39). Ans. (a) 2.3852 (exact: 2.3818), (b) 213.9934 (205.7061): (e) 0.3606 (0.3594); (d) 86.4762 (859703): (e) 92.0092 (101.7364) (f) 0.004869 (0.00479): (g) 005333 (005330); (h) 0.07391 (0.07387) (i) 89125 (8.8675): U) 5.5545 (5.5541); (k) 70591 (70146) 3.19 How many years (a whole nymbri uill

Explanation / Answer

This question is basically just "putting values into the expression" type. The only trouble is to extract the formula from the given ones. The question does not have full information, like the reference mentioned Appendix A where we can find the valuse of (A/P, i%, n) for different i and n. So I have just derived the required expressions to solve the question.

3.16 (A/F, i%, n) = (A/P, i%, n ) * ( P/F, i%, n) = (A/P, i%, n ) * (1 / ((1+i)^n) ) . Putting different values into this expression will give results.

Either use values from table in Appendix or by (A/P, i%, n)= { (i*((1+i)^n)) / (((1+i)^n) -1)} directly putting this expression into above and putting the values for i and n will give result.

a) (A/F, 4%, 20)=  { (0.04*((1+0.04)^20)) / (((1+0.04)^20) -1)} * {1/((1+0.04)^20)} = 0.03359

similarly for all other options.

3.17 The mentioned (3.6) is the expression given inside the chapter and not the problem 3.6, so check inside the chapter and use equation 3.6 to solve this.

Or directly putting the values in the following expression will give results:

(A/P, i%, n)= { (i*((1+i)^n)) / (((1+i)^n) -1)}

(A/P, 8%, 80)= { (0.08*((1+0.08)^80)) / (((1+0.08)^80) -1)}=0.08017=0.0802

and similarly for other parts.

3.18 For linear interpolation you have to see between which range the values of i and n occurs in the given table and then accordingly find out the value of the factors for the exact i and n value assuming the relationship is linear.

Exact values can be found out by using factor formulas

(F/A, i, n) = [(((1+i)^n)-1) / i ];

(A/P, i%, n)= { (i*((1+i)^n)) / (((1+i)^n) -1)}

(A/G , i, n)=[ (1/i) - (n/(((1+i)^n)-1))];

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