Trent receives a check for $20,000 from his parents for his 20th birthday. He de

Question

Trent receives a check for $20,000 from his parents for his 20th birthday. He decides to deposit this money into an account earning a 9% interest rate compounded monthly, forever.

8 years later, he decides to take $40,000 out of this account. He decides to use this money to make equal payments every year into a separate account earning annual interest until he turns 50.

Trent wants to throw an elaborate 50th birthday party and estimates that it will cost $150,000. If he uses solely the combined sums in both accounts at the time he turns 50, what annually compounded interest rate must he earn in the second account to be able to fund his birthday bash?

Explanation / Answer

978

By trial and error and changing the interest rate we get 7.171% annually to get $150000 at the end of his 50th birthday.

P $20,000.00 I 7.171% I(monthly) 0.60% First eight years 1 20150 2 20301 3 20453 4 20607 5 20761 6 20917 7 21074 8 21232 9 21391 10 21552 11 21713 12 21876 13 22040 14 22206 15 22372 16 22540 17 22709 18 22879 19 23051 20 23224 21 23398 22 23573 23 23750 24 23928 25 24108 26 24289 27 24471 28 24654 29 24839 30 25025 31 25213 32 25402 33 25593 34 25785 35 25978 36 26173 37 26369 38 26567 39 26766 40 26967 41 27169 42 27373 43 27578 44 27785 45 27994 46 28203 47 28415 48 28628 49 28843 50 29059 51 29277 52 29497 53 29718 54 29941 55 30165 56 30392 57 30620 58 30849 59 31081 60 31314 61 31548 62 31785 63 32023 64 32264 65 32506 66 32749 67 32995 68 33243 69 33492 70 33743 71 33996 72 34251 73 34508 74 34767 75 35027 76 35290 77 35555 78 35822 79 36090 80 36361 81 36634 82 36908 83 37185 84 37464 85 37745 86 38028 87 38313 88 38601 89 38890 90 39182 91 39476 92 39772 93 40070 94 40371 95 40673 96 40978 -40000 Amount at the end of 8 year period

978

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