You have just had your 30th birthday. You have two children, one of which will g
ID: 2780973 • Letter: Y
Question
You have just had your 30th birthday. You have two children, one of which will go to college 10 years from now and require four beginning-of-the-year payments for college expenses of $10,000, $11,000, $12,000, and $13,000. Your second child will go to college 15 years from now and require four beginning-of-the-year payments for college expenses of $15,000, $16,000, $17,000, and $18,000. In addition, you plan to retire in 30 years. You want to be able to withdraw $50,000 per year (at the end of each year) from an account throughout your retirement. You expect to live 20 years beyond retirement. The first withdrawal will occur on your 61st birthday. What equal, annual, and end-of-the-year amount must you save for each of the next 30 years to meet these goals, if all savings earn a 13% annual rate of return? How do I do this on a financial calculator?
Explanation / Answer
Annual Equal Instalment would be $3,778.54 Age of Mine Withdrawal 1/(1.13)n PV 40 10,000 0.29459 2,945.88 41 11,000 0.26070 2,867.67 42 12,000 0.23071 2,768.47 43 13,000 0.20416 2,654.14 45 15,000 0.15989 2,398.36 46 16,000 0.14150 2,263.94 47 17,000 0.12522 2,128.70 48 18,000 0.11081 1,994.62 61 50,000 0.02262 1,131.20 62 50,000 0.02002 1,001.06 63 50,000 0.01772 885.89 64 50,000 0.01568 783.98 65 50,000 0.01388 693.78 66 50,000 0.01228 613.97 67 50,000 0.01087 543.33 68 50,000 0.00962 480.83 69 50,000 0.00851 425.51 70 50,000 0.00753 376.56 71 50,000 0.00666 333.24 72 50,000 0.00590 294.90 73 50,000 0.00522 260.97 74 50,000 0.00462 230.95 75 50,000 0.00409 204.38 76 50,000 0.00362 180.87 77 50,000 0.00320 160.06 78 50,000 0.00283 141.65 79 50,000 0.00251 125.35 80 50,000 0.00222 110.93 PV of the Total Withdrawal(A) 29,001.20 Discount Factorfor 50 years at 13% (B) 7.67524 Annual Equal Contribution (A/B) 3,778.54 Working Note: Discount Factor table for 13% 1/(1.13)n Year Age of Mine Discount Factor 0 30 1 31 0.88496 2 32 0.78315 3 33 0.69305 4 34 0.61332 5 35 0.54276 6 36 0.48032 7 37 0.42506 8 38 0.37616 9 39 0.33288 10 40 0.29459 11 41 0.26070 12 42 0.23071 13 43 0.20416 14 44 0.18068 15 45 0.15989 16 46 0.14150 17 47 0.12522 18 48 0.11081 19 49 0.09806 20 50 0.08678 21 51 0.07680 22 52 0.06796 23 53 0.06014 24 54 0.05323 25 55 0.04710 26 56 0.04168 27 57 0.03689 28 58 0.03264 29 59 0.02889 30 60 0.02557 31 61 0.02262 32 62 0.02002 33 63 0.01772 34 64 0.01568 35 65 0.01388 36 66 0.01228 37 67 0.01087 38 68 0.00962 39 69 0.00851 40 70 0.00753 41 71 0.00666 42 72 0.00590 43 73 0.00522 44 74 0.00462 45 75 0.00409 46 76 0.00362 47 77 0.00320 48 78 0.00283 49 79 0.00251 50 80 0.00222 Total 7.67524
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