need help pls How long will it take for 2900 to grow to 2500

need help pls

How long will it take for $2900 to grow to $25,000 at an interest rate of 45% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

Solution

The formula for continuous compounding is A = Pe^rt , where P is the principal amount (initial investment), r is the rate of interest ( in decimals), t is time ( number of years) and A is the amount after time t. Here, P = $ 2900, r = 4.5 % = 4.4/100 = 0.045, and A = $ 25000. Therefore, we have 25000 = 2900e^0.045t or, e^0.045t = 25000/2900 = 250/29 = 8.620689655. On taking natural logarithms of both the sides, we have 0.045t ln e = ln 8.620689655 or, 0.045t = 2.154165088( as ln e = 1). Then t = 2.154165088/ 0.045 = 47.87033529 = 47 87 years ( on rounding off to the nearest hundredth)