Question

what rate of interest compounded annually is required to double an investment in 3 years? please help!!!

Answer 1

\(\Huge\color{blue}{ \sf A=P(1+\frac{r}{n} )^{nt} }\)

P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year

\(\Huge\color{blue}{ \sf 100=50(1+\frac{r}{1} )^{1\times 3 }}\)

\(\Huge\color{blue}{ \sf 100=50(1+\frac{r}{1} )^{3 }}\)

\(\Huge\color{blue}{ \sf 100=50(\frac{1+r}{1} )^{3 }}\) (in this step I divide both sides by 50 )

\(\Huge\color{blue}{ \sf 2=(\frac{1+r}{1} )^{3 }}\)

\(\Huge\color{blue}{ \sf 2=\frac{(1+r)^3}{1^3} }\)

\(\Huge\color{blue}{ \sf 2=\frac{(1+r)^3}{1} }\)

\(\Huge\color{blue}{ \sf 2= (1+r)^3 }\)

\(\Huge\color{blue}{ \sf \sqrt[3]{2^3} =(1+r)^3 }\) (in this step I take cube root of both sides )
....

Answer 2

\(\Huge\color{blue}{ \sf 2= (1+r)^3 }\)

\(\Huge\color{blue}{ \sf \sqrt[3]{2} =(1+r) }\) (in this step I take cube root of both sides )

\(\Huge\color{blue}{ \sf \sqrt[3]{2} =1+r }\)

\(\Huge\color{blue}{ \sf \sqrt[3]{2} -1=r }\)

\(\Huge\color{blue}{ \sf (~~~~~ \sqrt[3]{2} ≈1.26 ~~~) }\)