MC Qu. 6-A9 You are considering an annuity which costs... You are considering an
ID: 2641081 • Letter: M
Question
MC Qu. 6-A9 You are considering an annuity which costs...
You are considering an annuity which costs $90,500 today. The annuity pays $6,200 a year. The rate of return is 6 percent. What is the length of the annuity time period? (Do not round intermediate calculations.)
rev: 09_26_2013_QC_36309
You are considering an annuity which costs $90,500 today. The annuity pays $6,200 a year. The rate of return is 6 percent. What is the length of the annuity time period? (Do not round intermediate calculations.)
Explanation / Answer
The correct answer is 35.80 years.
The annuity gives a annual return of 6%. However the yearly payout is $ 6200 which is higher than 6 % p.a. Thus the annuity will get written of over a period of time as per the following schedule.
Year Opening Return @ 6% Payout Closing Balance A B = A * 6% C (given) D = A+B-C 1 90,500.00 5,430.00 6,200.00 89,730.00 2 89,730.00 5,383.80 6,200.00 88,913.80 3 88,913.80 5,334.83 6,200.00 88,048.63 4 88,048.63 5,282.92 6,200.00 87,131.55 5 87,131.55 5,227.89 6,200.00 86,159.44 6 86,159.44 5,169.57 6,200.00 85,129.00 7 85,129.00 5,107.74 6,200.00 84,036.75 8 84,036.75 5,042.20 6,200.00 82,878.95 9 82,878.95 4,972.74 6,200.00 81,651.69 10 81,651.69 4,899.10 6,200.00 80,350.79 11 80,350.79 4,821.05 6,200.00 78,971.84 12 78,971.84 4,738.31 6,200.00 77,510.15 13 77,510.15 4,650.61 6,200.00 75,960.75 14 75,960.75 4,557.65 6,200.00 74,318.40 15 74,318.40 4,459.10 6,200.00 72,577.50 16 72,577.50 4,354.65 6,200.00 70,732.15 17 70,732.15 4,243.93 6,200.00 68,776.08 18 68,776.08 4,126.56 6,200.00 66,702.65 19 66,702.65 4,002.16 6,200.00 64,504.81 20 64,504.81 3,870.29 6,200.00 62,175.09 21 62,175.09 3,730.51 6,200.00 59,705.60 22 59,705.60 3,582.34 6,200.00 57,087.94 23 57,087.94 3,425.28 6,200.00 54,313.21 24 54,313.21 3,258.79 6,200.00 51,372.01 25 51,372.01 3,082.32 6,200.00 48,254.33 26 48,254.33 2,895.26 6,200.00 44,949.59 27 44,949.59 2,696.98 6,200.00 41,446.56 28 41,446.56 2,486.79 6,200.00 37,733.35 29 37,733.35 2,264.00 6,200.00 33,797.36 30 33,797.36 2,027.84 6,200.00 29,625.20 31 29,625.20 1,777.51 6,200.00 25,202.71 32 25,202.71 1,512.16 6,200.00 20,514.87 33 20,514.87 1,230.89 6,200.00 15,545.76 34 15,545.76 932.75 6,200.00 10,278.51 35 10,278.51 616.71 6,200.00 4,695.22 36 4,695.22 281.71 6,200.00 (1,223.07) 5,918.29 Note: Erosion of capital in 36th year(Bal as at 35th yr + deficiency at the end of 36th yr
4695+1223.07) 5,918.29 Balance capital to recover 4,695.22 Recovery Period ( 5918/12 *4695.22) 9.52 months % of year (9.52/12 *100) 0.79 year Total period 35 + .80 = 35.80 years
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.