Assume that you have developed the next investment plan for your saving account
ID: 2422099 • Letter: A
Question
Assume that you have developed the next investment plan for your saving account (with an interest rate of 6% per year, compunded semiannually):
- Make eight annual deposits of X dollars each, starting now, making the last deposit at the end of year seven
- Make a deposit of $3000.00 at year 10
- Starting at year 12 make 8 consecutive equal annual withdrawals of $3000.00
a) draw the cash flow diagram
b) Determine the amount of the unknown deposits such as that the total money withdrawn is equvalent to the total money deposited
Explanation / Answer
Total money withdrawn is (3000X8=) $24000
Total money deposited = Total money withdrawn = $ 24000
At year 10 $3000 deposited, therefore remaining money deposited is (24000-3000=) $21000
Eight Equal annual deposit, thus yearly deposit = 21000/8 = $2625
Thus unknown deposit is $2625
a) cash flow diagram
Year Opening Bal Principal Withdrawal Interest Last Deposit Closing Bal 1st Half @3% 2nd Half @3% 1 - 2,625.00 - 78.75 81.11 - 2,784.86 2 2,784.86 2,625.00 - 162.30 167.16 - 5,739.32 3 5,739.32 2,625.00 - 250.93 258.46 - 8,873.71 4 8,873.71 2,625.00 - 344.96 355.31 - 12,198.98 5 12,198.98 2,625.00 - 444.72 458.06 - 15,726.76 6 15,726.76 2,625.00 - 550.55 567.07 - 19,469.38 7 19,469.38 2,625.00 - 662.83 682.72 2,625.00 26,064.93 8 26,064.93 - - 781.95 805.41 - 27,652.29 9 27,652.29 - - 829.57 854.46 - 29,336.31 10 29,336.31 3,000.00 - 970.09 999.19 - 34,305.59 11 34,305.59 - - 1,029.17 1,060.04 - 36,394.80 12 36,394.80 - 3,000.00 1,001.84 1,031.90 - 35,428.55 13 35,428.55 - 3,000.00 972.86 1,002.04 - 34,403.45 14 34,403.45 - 3,000.00 942.10 970.37 - 33,315.92 15 33,315.92 - 3,000.00 909.48 936.76 - 32,162.15 16 32,162.15 - 3,000.00 874.86 901.11 - 30,938.13 17 30,938.13 - 3,000.00 838.14 863.29 - 29,639.56 18 29,639.56 - 3,000.00 799.19 823.16 - 28,261.91 19 28,261.91 - 3,000.00 757.86 780.59 - 26,800.36