Question

Jasmine deposits 1000 into a savings account paying nominal interest rate of 6 percent compounded three times a year. She decides to deposit the same amount at the beginning of each third of the year for 20 years. The interest earned from this account is withdrawn at the end of each year only and reinvested into another account earning AEIR 8%. Find the accumulated value of Jasmine’s money in both accounts at the end of the 20 years.

Answer 1

K11 X fo =J9+J10+J11 C D E F G H - K L M N 0 P 1 2 2% (6/3) 3 Effective Interest for Period of one third of a year Future Value of Reinvestment at end of 20 years (Reinvested Amount)*(1.08^(20-N)) N=Year of Reinvestment 4 5 6 A B C=A*2% D B+C-D N R FV=R*(1.08^(20-N)) Amount Reinvested 7 Year Future value 8 1 524.82 1 2 1219.71 9 10 121.61 305.23 488.86 672.48 1 3 1808.78 11 1 4 2303.88 12 2 5 856.10 2715.71 Period(one Beginning Ending third of year) Balance Deposit Interest Withdrawal Balance Year 0 0 1000 0 0 1000 1 1000.00 1000 20 2020 2 2020.00 1000 40.4 3060.40 3 3060.40 1000 61.208 121.61 4000.00 4 4000.00 1000 80 5080.00 5 5080.00 1000 101.6 6181.60 6 6181.60 1000 123.632 305.23 7000.00 7 7000.00 1000 140 8140.00 8 8140.00 1000 162.8 9302.80 9 9302.80 1000 186.056 488.86 10000.00 10 10000.00 1000 200 11200.00 11 11200.00 1000 224 12424.00 13 2 6 3053.88 14 2 7 3327.06 1039.7 1223.35 1406.98 1590.60 8 3 3 9 15 16 17 18 3543.00 3708.70 3830.42 3913.75 3 10 4 11 1774.22 1957.85 2141.47 19 4 12 3963.72

K32 X f =J30+J31+J32 C D E F G H K L M N 0 Р 3 9 10 17 18 4 10 11 4 11 12 19 20 21 4 12 13 9302.80 10000.00 11200.00 12424.00 13000.00 14260.00 15545.20 16000.00 186.056 200 224 248.48 260 285.2 310.904 13 14 1774.22 1957.85 2141.47 2325.10 2508.72 2692.34 2875.97 3830.42 3913.75 3963.72 3984.81 3981.02 3955.94 3912.72 5 22 14 5 5 15 16 23 24 25 15 16 6 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 320 17 3059.59 3243.22 3854.20 3782.89 6 17 18 17320.00 18666.40 26 6 18 346.4 373.328 380 19 3700.99 488.86 10000.00 11200.00 12424.00 672.48 13000.00 14260.00 15545.20 856.10 16000.00 17320.00 18666.40 1039.7 19000.00 20380.00 21787.60 1223.35 22000.00 23440.00 24908.80 1406.98 25000.00 26500.00 28030.00 1590.60 28000.00 29560.00 3426.84 3610.46 7 19 19000.00 20 3610.46 27 28 29 7 20 407.6 SUM 64696.46 7 21 435.752 30 8 22 20380.00 21787.60 22000.00 23440.00 24908.80 440 31 8 23 32 8 24 1000 468.8 498.176 500 33 9 25 34 26 530 9 9 25000.00 26500.00 28030.00 28000.00 1000 1000 1000 1000 35 27 28 560.6 560 36 10

K53 : f =J51+352 +353 с D E F G - J K L M N 10 28 10 29 36 37 38 39 30 10 11 11 31 H 28000.00 29560.00 31151.20 31000.00 32620.00 34272.40 34000.00 35680.00 40 32 41 11 33 42 34 43 12 12 12 35 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 29560.00 31151.20 1774.22 31000.00 32620.00 34272.40 1957.85 34000.00 35680.00 37393.60 2141.47 37000.00 38740.00 40514.80 2325.10 40000.00 41800.00 43636.00 2508.72 43000.00 44860.00 36 44 45 13 37 560 591.2 623.024 620 652.4 685.448 680 713.6 747.872 740 774.8 810.296 800 836 872.72 860 897.2 935.144 920 958.4 46 13 38 47 39 37393.60 37000.00 38740.00 40514.80 40000.00 41800.00 43636.00 13 14 48 40 49 14 41 14 42 50 51 43 43000.00 15 15 15 44 52 53 54 55 56 45 46 16 44860.00 46757.20 46000.00 47920.00 49878 un 1000 1000 1000 1000 1000 46757.20 2692.34 46000.00 47920.00 49878.40 287597 49000.00 16 47 16 48 997 568

K68 X =J66+J67+J68 с D E F G H - L M 45 15 16 46 16 47 16 48 53 54 55 56 57 58 59 60 46757.20 46000.00 47920.00 49878.40 49000.00 50980.00 52999.60 52000.00 17 49 17 50 17 51 18 52 J 1000 935.144 1000 920 1000 958.4 1000 997.568 1000 980 1000 1019.6 1000 1059.992 1000 1040 1000 1080.8 1000 1122.416 1000 1100 1000 1142 1000 1184.84 1000 1160 1000 1203.2 1247.264) K 2692.34 46000.00 47920.00 49878.40 2875.97 49000.00 50980.00 52999.60 3059.59 52000.00 54040.00 56120.80 3243.22 55000.00 57100.00 59242.00 3426.84 58000.00 60160.00 62363.20 3610.46| 60000.00 61 18 53 54040.00 62 18 54 56120.80 63 19 55 55000.00 64 19 56 57100.00 19 57 59242.00 58000.00 20 58 20 60160.00 65 66 67 68 69 70 59 60 62363.20 20 ACCUMULATED VALUE IN ACCOUNT WITH APR 6% 60000.00 ACCUMULATED VALUE IN ACCOUNT WITH AEIR 8% 64696.46 TOTAL ACCUMULATED AMOUNT 124696.46 71 72