SOLUTION: Hi I'd appreciate some help with this question. A taxi company must replace cars every 5 years at a cost of 450,000. The company decides to deposit 4000 at the beginning of

Question 744823: Hi
I'd appreciate some help with this question.
A taxi company must replace cars every 5 years at a cost of 450,000. The company decides to deposit 4000 at the beginning of each month into a fund for preperation.
i)Calculate the size of this fund after 5 years if the interest rate is fixed at 6% per annum.
ii)By how much does the company meet or exceed the target of 450,000.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The problem states:
A taxi company must replace cars every 5 years at a cost of 450,000. The company decides to deposit 4000 at the beginning of each month into a fund for preperation.
i)Calculate the size of this fund after 5 years if the interest rate is fixed at 6% per annum.
ii)By how much does the company meet or exceed the target of 450,000.
There are 5 * 12 months in 5 years, this equals 60
now 60 * 4000 = 240000 deposited by the company
now we turn to the 6% per annum calculation
each year totals with interest added
1) 12 * 4000 = 48000 + 6%*48000 = 48000 + 2880 = 50880
2) 50880 + 48000 = 98880 + 6%*98880 = 98880 + 5932.8 = 104812.8
3) 104812.8 + 48000 = 152812.8 + 6%*152812.8 = 152812.8 + 9168.768 = 161981.568
4) 161981.568 + 48000 = 209981.568 + 6%*209981.568 = 209981.568 + 12598.89408 = 222580.46208
5) 222580.46208 + 48000 = 270580.46208 + 6%*270580.46208 = 270580.46208 + 16234.8277248 = 286815.2898048
The company has exceeded its target by 286815.2898048 - 250000 = 36815.2898048
Notice that the company's target is a whole number so we round the result to the whole number
36815

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