$10000 was compounded annually at 12.5% p.a. and amounted to $52015.80. How many years did it take?
A=P(1+r)tA=P(1+r)^tA=P(1+r)t
52015.80=10000(1+0.125)t52015.80=10000(1+0.125)^t52015.80=10000(1+0.125)t
5.201580=[1+0.125]t5.201580=[1+0.125]^t5.201580=[1+0.125]t
5.201580=[1.125]t5.201580=[1.125]^t5.201580=[1.125]t
log5.201580=tlog(1.125)log5.201580=tlog(1.125)log5.201580=tlog(1.125)
t=log5.201580log1.125=14yearst=\frac{log5.201580}{log1.125}=14yearst=log1.125log5.201580=14years
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