If the interest is calculated yearly, then:
100,000×1.0625x=150,000,100,000×1.0625^x = 150,000,100,000×1.0625x=150,000,
log(1.0625)1.5=6.69\log(1. 0625) 1.5 = 6.69log(1.0625)1.5=6.69
years.
If the interest is paid monthly, then:
100,000×(1+0.0625/12)12x=150,000,100,000×(1 + 0.0625/12)^{12x} = 150,000,100,000×(1+0.0625/12)12x=150,000,
log(1.0052)1.5/12=6.51\log(1.0052) 1.5/12 = 6.51log(1.0052)1.5/12=6.51 years.
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