Please show each step how to work out. Thank you for the help! Mary would like t

Question

Please show each step how to work out. Thank you for the help!

Mary would like to save for retirement. She starts a money market account on her 28th birthday with $2,000 with an investment company which is guaranteed to earn at least 2% per year, compounded six-monthly. She would like to retire on her 67th birthday by being able to make 2 deposits per year. She starts the first deposit of $1,000 six months after her 28th birthday, followed by another $1,000 deposit six months later on her 29th birthday. She increases the deposit the next year by $100, and repeats the deposit pattern which ends on her 67th birthday. How much can she expect to have collected in her account on her 67th birthday? O $259,350 O $315,250 O$423,540 9 3 0 $546,630

Explanation / Answer

Calculations are made through Excel sheet as follows. Interest rate per period is 1%.

Age First Half Subtotal Interest Total Second Half Subtotal Interest 1% Total 28 0.00 0.00 0.00 0.00 1000.00 1000.00 10.00 1010.00 29 1000.00 2010.00 20.10 2030.10 1100.00 3130.10 31.30 3161.40 30 1100.00 4261.40 42.61 4304.02 1200.00 5504.02 55.04 5559.06 31 1200.00 6759.06 67.59 6826.65 1300.00 8126.65 81.27 8207.91 32 1300.00 9507.91 95.08 9602.99 1400.00 11002.99 110.03 11113.02 33 1400.00 12513.02 125.13 12638.15 1500.00 14138.15 141.38 14279.53 34 1500.00 15779.53 157.80 15937.33 1600.00 17537.33 175.37 17712.70 35 1600.00 19312.70 193.13 19505.83 1700.00 21205.83 212.06 21417.89 36 1700.00 23117.89 231.18 23349.07 1800.00 25149.07 251.49 25400.56 37 1800.00 27200.56 272.01 27472.56 1900.00 29372.56 293.73 29666.29 38 1900.00 31566.29 315.66 31881.95 2000.00 33881.95 338.82 34220.77 39 2000.00 36220.77 362.21 36582.98 2100.00 38682.98 386.83 39069.81 40 2100.00 41169.81 411.70 41581.51 2200.00 43781.51 437.82 44219.32 41 2200.00 46419.32 464.19 46883.51 2300.00 49183.51 491.84 49675.35 42 2300.00 51975.35 519.75 52495.10 2400.00 54895.10 548.95 55444.05 43 2400.00 57844.05 578.44 58422.49 2500.00 60922.49 609.22 61531.72 44 2500.00 64031.72 640.32 64672.04 2600.00 67272.04 672.72 67944.76 45 2600.00 70544.76 705.45 71250.20 2700.00 73950.20 739.50 74689.71 46 2700.00 77389.71 773.90 78163.60 2800.00 80963.60 809.64 81773.24 47 2800.00 84573.24 845.73 85418.97 2900.00 88318.97 883.19 89202.16 48 2900.00 92102.16 921.02 93023.18 3000.00 96023.18 960.23 96983.41 49 3000.00 99983.41 999.83 100983.25 3100.00 104083.25 1040.83 105124.08 50 3100.00 108224.08 1082.24 109306.32 3200.00 112506.32 1125.06 113631.39 51 3200.00 116831.39 1168.31 117999.70 3300.00 121299.70 1213.00 122512.70 52 3300.00 125812.70 1258.13 127070.82 3400.00 130470.82 1304.71 131775.53 53 3400.00 135175.53 1351.76 136527.29 3500.00 140027.29 1400.27 141427.56 54 3500.00 144927.56 1449.28 146376.84 3600.00 149976.84 1499.77 151476.60 55 3600.00 155076.60 1550.77 156627.37 3700.00 160327.37 1603.27 161930.64 56 3700.00 165630.64 1656.31 167286.95 3800.00 171086.95 1710.87 172797.82 57 3800.00 176597.82 1765.98 178363.80 3900.00 182263.80 1822.64 184086.44 58 3900.00 187986.44 1879.86 189866.30 4000.00 193866.30 1938.66 195804.96 59 4000.00 199804.96 1998.05 201803.01 4100.00 205903.01 2059.03 207962.04 60 4100.00 212062.04 2120.62 214182.66 4200.00 218382.66 2183.83 220566.49 61 4200.00 224766.49 2247.66 227014.15 4300.00 231314.15 2313.14 233627.30 62 4300.00 237927.30 2379.27 240306.57 4400.00 244706.57 2447.07 247153.63 63 4400.00 251553.63 2515.54 254069.17 4500.00 258569.17 2585.69 261154.86 64 4500.00 265654.86 2656.55 268311.41 4600.00 272911.41 2729.11 275640.53 65 4600.00 280240.53 2802.41 283042.93 4700.00 287742.93 2877.43 290620.36 66 4700.00 295320.36 2953.20 298273.56 4800.00 303073.56 3030.74 306104.30 67 4800.00 310904.30 3109.04 314013.34

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