Question

Today you inherit an account with a balance of $5,400. For a while you don't do anything with the account but it continues to accrue interest. Exactly 21 months from today you start an ambitious savings plan and deposit $190 into the account. You plan to deposit that much each month. Exactly 45 months from today you reconsider your plan, make your last deposit, and make no additional deposits. You and it continues to accrue interest at a rate of 75% compounded monthly You finally close the account exactly 8 years from today. How much is the total accumulation? $8.457 a $15,972 b. $10,909 c $12,000 d $13,200 $14,520

Answer 1

$5,400.00 0.63% per month Balance today Interest rate (7.5%) Step 1: Balance after 21 months = $5400 x (1.0063)^21 $6,161.28 = Monthly Deposits from 21st month = $ 190.00 Step 2: Computation of Balance after 45 months Closing Month Opening Bal Deposit Interest Balnace 21 $ 6,161.28 $ 190.00 $ 38.51 $ 6,389.78 22 $ 6,389.78 $ 190.00 $ 39.94 $ 6,619.72 23 $ 6,619.72 $ 190.00 $ 41.37 $ 6,851.09 24 $ 6,851.09 $190.00 $ 42.82 $ 7,083.91 25 $ 7,083.91 $ 190.00 $ 44.27 $ 7,318.19 26 $ 7,318.19 $ 190.00 $ 45.74 $ 7,553.93 27 $ 7,553.93 $ 190.00 $ 47.21 $ 7,791.14 28 $ 7,791.14 $190.00 $ 48.69 $ 8,029.83 29 $ 8,029.83 $ 190.00 $ 50.19 $ 8,270.02 30 $ 8,270.02 $ 190.00 $ 51.69 $ 8,511.71 31 $ 8,511.71 $190.00 $ 53.20 $ 8,754.91 32 $ 8,754.91 $190.00 $ 54.72 $ 8,999.62 33 $ 8,999.62 $ 190.00 $ 56.25 $ 9,245.87 34 $ 9,245.87 $190.00 $ 57.79 $ 9,493.66 35 $ 9,493.66 $ 190.00 $ 59.34 $ 9,742.99 36 $ 9,742.99 $ 190.00 $ 60.89 $ 9,993.89 37 $ 9,993.89 $ 190.00 $ 62.46 $ 10,246.35 38 $ 10,246.35 $ 190.00 $ 64.04 $ 10,500.39 39 $ 10,500.39 $190.00 $ 65.63 $10,756.02 40 $ 10,756.02 $ 190.00 $ 67.23 $ 11,013.24 41 $ 11,013.24 $ 190.00 $ 68.83 $ 11,272.07 42 $ 11,272.07 $ 190.00 $ 70.45 $ 11,532.52 43 $ 11,532.52 $ 190.00 $ 72.08 $ 11,794.60 44 $ 11,794.60 $ 190.00 $ 73.72 $ 12,058.32 45 $ 12,058.32 $ 190.00 $ 75.36 $ 12,323.68 Step 3: Future value of $12,323.68 after futher 26 months $12,323 x (1.0063)^26 14509.57871 As the answer is near to $14,520. Option e. $14,520 should be the correct answer Note: The difference in final answers arise due to rounding of the intermediate calculations

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