Question

Problem 4: An estate worth $1,500,000 and earning 24% per annum compounded monthly makes equal payments of $50,000 at the end of each month to Betty and Bob. a. Algebraically determine how many payments they will receive. b. Algebraically determine the amount of the last payment that will settle the estate. Mornan 1907

Answer 1

Answer- Given data, worth pve $1500000 Annuity is $50,000 Interest rate is 20% per annum Compounded monthly, hence noll for effective interest rate. Неме, Essechive interest rate = (1+ 24:14.)"; > (1+2y.)?, = (1002)2-1 - 0.2682 = 26.821. Monthly rate = 26.82-4, = 2235.1. Hence, PV = AX (1-CH2X)-)/ 1500000 = 50000 XC1-C1+ 22354.)")/2.2354.

1500000 X QI02235 31-CH0.02235) 50000 0.6705 = 1-(1.02235) (1002235) * = 1-0.6705. (11 02235) * = 0.3295 Applying log on both sides, 109 (1002235) = 109 0.3295 -n log10022 35 = log 0.3295 70X0.0096 +0:482) n=0.4821 0.0096. n = 50.22 Therefore, total number of payments will be Coplast payment is for (50.22 -50). R = 0.22 month last payment = 0.22 X 50,000 -$ 11,000 therefore, the amount of the last payment is [$ 11,0007