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zzz [600]
3 years ago
13

Danny decided to invest his $500 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded

quarterly. If he deposits the entire $500 and does not deposit or withdraw any other amount, how long will it take him to double his money in the account? Round your answer to the nearest tenth of a year. It will take Answer years for his investment to double.
Mathematics
1 answer:
Blababa [14]3 years ago
5 0
Present value, PV = $500
Future value, FV = 2*PV = 2*500 = $1,000
Rate, r = 4% = 0.04
Compounding times in a year, n = 4 (compounded quarterly)
Time, t = ??

The future value expression is stated as:
FV = PV (1+r/n)^nt

Substituting;
1000 = 500 (1+0.04/4)^4t
2 = (1.01)^4t
ln 2 = 4t ln 1.01
0.6931 = 4t* 0.00995
0.6931 = 0.0398t
t = 17.414 years

Time required for the amount to double is 17.41 years.
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Answer:

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Now we have \frac{3\cdot3}{4\cdot3} = \frac{9}{12}. To add 9/12 and 5/12, we keep the denominator the same, and add the numerators, getting \frac{9+5}{12} =\frac{14}{12}. This is greater than 1, so we can take 12/12 from 14/12, and make it 1 \frac{2}{12}. If we then add 3, we get 4 \frac{2}{12}, which simplifies to 4 \frac{1}{6}

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