Question 1202792
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12 & 1/2 = 12.5
12.5% = 0.125 in decimal form


If you're working with simple interest, then,
A = P*(1+r*t)
2P = P*(1+0.125*t)
2 = 1+0.125*t
1+0.125*t = 2
0.125*t = 2-1
0.125*t = 1
t = 1/0.125
t = 8
It will take 8 years for the money to double at 12.5% simple interest.



If you're working with compound interest, when the money is compounded annually, then,
A = P*(1+r/n)^(n*t)
2P = P*(1+0.125/1)^(1*t)
2 = (1.125)^t
log(2) = log( (1.125)^t )
log(2) = t*log(1.125)
t = log(2)/log(1.125)
t = 5.88494919236171
t = 5.8849
It will take about 5.8849 years for the money to double at 12.5% compound interest, when the money is compounded annually.



If you're working with compound interest, when the money is compounded semi-annually, then,
A = P*(1+r/n)^(n*t)
2P = P*(1+0.125/2)^(2*t)
2 = (1.0625)^(2t)
log(2) = log( (1.0625)^(2t) )
log(2) = 2t*log(1.0625)
t = log(2)/(2*log(1.0625))
t = 5.71671343912647
t = 5.7167
It will take about 5.7167 years for the money to double at 12.5% compound interest, when the money is compounded semi-annually.


I'll skip the steps for other cases of n, but you should get these approximate time values.
<table border = "1" cellpadding = "5"><tr><td>N</td><td>T</td></tr><tr><td>1</td><td>5.8849</td></tr><tr><td>2</td><td>5.7167</td></tr><tr><td>4</td><td>5.6314</td></tr><tr><td>12</td><td>5.5740</td></tr><tr><td>365</td><td>5.5461</td></tr></table>
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