Q 12.17 (chap 12) on page 31 has been solved by finding PV of annuity and accumulating @ 8% for 15 yes If I want to arrive at the answer directly by accumulating the annuity, how do I do so? Which rates do I use?
By using exact formula it can be solved as follows: = \( 1500(1.08)^{15} + 1500(1.06)(1.08)^{14} + \dots + 1500(1.06)^{14}(1.08)\) we need to make this equation look like this.. = \( (1+i)^{15}+ (1+i)^{14} + \dots + (1+i)\) i.e. divide numerator and denominator of above equation by (1.06)^15 =1500*\({1.06}^{15}\){ \( (1.08/1.06)^{15} + (1.08/1.06)^{14} + \dots + (1.08/1.06)\)} = 1500 x \({1.06}^{15}\) \(\require{enclose}\ddot {s}_{\enclose{actuarial}{15}}\) @1.88679 {i.e. 1.08/1.06 =1.0188679} = 1500 x \({1.06}^{15}\) x \(\frac{({1+0.0188679})^{15} -1 }{0.0188679/1.0188679} \) = 62,824.47 pounds.
