Question

you lend a friend 10,000 dollars for which your friend will repay you 27,027 dollars at the end of 5 years. What interest rate are you charging your friend?

Answer 1

Answer:

The interest rate is "21.999%".

Explanation:

The given values are:

Amount lent,

= 10,000

Amount repaid,

= 27,027

Years (n),

= 5

As we know,

⇒  $Amount \ repaid = Amount \ lent\times (1+r)^n$

On substituting the given values, we get

⇒                $27,027=10,000\times (1+r)^5$

⇒                  $\frac{27,027}{10,000}=(1+r)^5$

⇒                 $2.7027=(1+r)^5$

⇒                 $1+r = (2.7027)^{(1/5)}$

⇒                 $1+r=1.21999$

On subtracting "1" from both sides, we get

⇒          $1+r-1=1.21999-1$  

⇒                      $r=0.21999$

i.e.,

⇒                      $r=21.999 \ percent$