Question

Mrs. Williams finds that she has two options for investing $31,000.03 for fifteen years. The first option is to deposit the $31,000.03 into a fund earning a nominal rate of discount d⁽⁴⁾ payable quarterly. The second option is to purchase an annuity-immediate with 15 level annual payments, the annuity payments computed using an annual effective rate of 6%, and then when she gets an annuity payment, to immediately invest it into a fund earning an annual effective rate of 3%. Mrs. Williams calculates that the second option produces an accumulated value that is $1,500 more than the accumulated value yielded by the first option. Calculate d⁽⁴⁾. (Round your answer to two decimal places.)

d⁽⁴⁾ = ____%

Answer 1

The given problem, Cleposit of Money $ -=-39,000-03 - an ammunity - Pimmediate = 15 level annual payments effective. vate per year & 6%=> ) 6 = 0·06 let Az Ammunity She civil received eacı yeur 31,000.03 @ICE (tocis) 31;00003 2.3965) 31,000'03 5.0 (-0340540) A = 31,000.03 = 31918:45: 971225 Re invest this amaunt at intrest rate 4% 4 ) 0:04 * 31918.45(1.049+7.04'} t ...05€ +') 5) 31918.45 * 20.0236 =) 63, 9120.27 Accumlated of finst option: 006 - 63,912:22-1500-) 62,412•22. 62,412.222 31000:03/1+ du at 621412-22 x 60 31.000 03 d4 =.0.03.587