Solve the given problem releated to continuous compounding interest.
How long will it take $$ 1, 000$ to triple if it is invested at an annual interest rate of $5.7 %$ compounded continuously? Round to the nearest year. $yr$

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So, it will take approximately $19$ years for the investment to triple.

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Step 1 ：We are given that the principal amount (P) is $1000, t h e a m o u n t o f m o n e y a c c u m u l a t e d a f t e r n y e a r s, i n c l u d i n g i n t e r e s t (A) i s$ 3000, and the annual interest rate (r) is 5.7% or 0.057 in decimal form. We need to find the time the money is invested for in years (t).

Step 2 ：The formula for continuous compounding interest is $A = P e^{r t}$ .

Step 3 ：We can rearrange this formula to solve for t, giving us $t = \frac{1}{r} \ln (\frac{A}{P})$ .

Step 4 ：Substituting the given values into this formula, we get $t = \frac{1}{0.057} \ln (\frac{3000}{1000})$ .

Step 5 ：Solving this equation gives us $t \approx 19$ .

Step 6 ：So, it will take approximately $19$ years for the investment to triple.

Solve the given problem releated to continuous compounding interest.How long will it take $1,000 to triple if it is invested at an annual interest rate of 5.7% compounded continuously? Round to the nearest year. yr

Answer

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Solve the given problem releated to continuous compounding interest.
How long will it take $$ 1, 000$ to triple if it is invested at an annual interest rate of $5.7 %$ compounded continuously? Round to the nearest year. $yr$