Lucas is 18 years old and wants to have $50000 saved by the time he is 21.?
2016-11-07 6:37 pm
If he puts $1000 into an investment every three months that pays 6.05 percent compounded quarterly, how much must he already have saved in order to reach his goal?
回答 (1)
2016-11-07 7:08 pm
We asssume Lucas makes 13 deposits, one today on his 18th birthday, and the last one on his 21st birthday. The sum of their value is the sum of a geometric series with a multiplier of 1+0.0605/4 = 1.015125. That sum is
.. 1000*(1.015125^13 -1)/(1.015125 -1) = 14,247.72
This amount is 35,752.28 short of Lucas's goal. If Lucas can earn the same interest on the amount he already has saved, that amount must be
.. 35,752.28/(1.015125^12) = 29, 858.60
Lucas must have already saved $29,858.60 if he can earn the same interest on that amount. If Lucas does not earn interest on the amount already saved, he must have $35,752.28.
.. 1000*(1.015125^13 -1)/(1.015125 -1) = 14,247.72
This amount is 35,752.28 short of Lucas's goal. If Lucas can earn the same interest on the amount he already has saved, that amount must be
.. 35,752.28/(1.015125^12) = 29, 858.60
Lucas must have already saved $29,858.60 if he can earn the same interest on that amount. If Lucas does not earn interest on the amount already saved, he must have $35,752.28.
收錄日期: 2021-04-21 23:55:40
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https://hk.answers.yahoo.com/question/index?qid=20161107103700AAmXDEm