Determine the time needed tor 1400 to grow to 2600 it the in

Determine the time needed tor $1400 to grow to $2600 it the interest rate is 3% compounded continuously.

Solution

The formula for continuous compounding of interest is A = Pe^rt , where P is the initial amount/principal, r is the rate of interest in decimals, t is the period in years and A is the amount after t years. Here, P = $ 1400, A = $ 2600 and r = 3 % = 0.03. Then 2600 = 1400e^0.03t or, 2600/1400 = e^0.03t or, e^0.03t   = 1.857142857. On taking natural logarithms of both the sides, we have 0.03t ln e = ln 1.857142857 , or, 0.03 t = 0.619039208 ( as log a^b = b log a and ln e = 1) so that t = 0.619039208/0.03 = 20.63464028 years= 20 years, 7.62 months approximately