How long will it take an investment of $10 000 to double at an interest rate of 7.5% pa compounded monthly?
20,000 = 10,000(1 + 0.00625)^{n}
2 = (1 + 0.00625)^{n
}
then start ‘guessing and checking’ values for n to make it work
n = 100: (1 + 0.00625)^{100 } = 1.86 too low
n = 150: (1 + 0.00625)^{150 } = 2.54 too high
n = 125: (1 + 0.00625)^{125 } = 2.17 too high
n = 115: (1 + 0.00625)^{115 } = 2.04 too high
n = 110: (1 + 0.00625)^{110 } = 1.98 too low
n = 111: (1 + 0.00625)^{111 } = 1.997 too low
n = 112: (1 + 0.00625)^{112 } = 2.00 too low
n = 112 months
$$\frac{112}{12}
= 9.3 years