What was the interest rate if your balance on an investment of 27, 750 at the end of six years is 41,070?
Answer (1)
[tex]\large{\bold{SOLUTION}}[/tex]The formula for future value is[tex]\blue{\Large\boxed{\sf{FV = PV(1+r) ^{n} }}}[/tex]In the problem, we are trying to find the value of r which is the annual interest rate (assuming the investment only bears sinple interest)Step 1: Derive the formula by isolating the variable r in the equation[tex]\sf{\dfrac{FV}{PV} = \dfrac{ PV(1 + r)^{n}}{PV} }[/tex][tex]\sf{\dfrac{FV}{PV} = (1 + r)^{n} }[/tex][tex]\sf{(\dfrac{FV}{PV}) ^{ \frac{1}{n} }= ((1 + r)^{n})^{ \frac{1}{n} } }[/tex][tex]\sf{(\dfrac{FV}{PV})^{ \frac{1}{n} } = 1 + r }[/tex][tex]\sf{(\dfrac{FV}{PV})^{ \frac{1}{n} } - 1= r }[/tex]Step 2: Plug in the values[tex]\sf{r = ( \dfrac{FV}{PV})^{ \frac{1}{n} } - 1 }[/tex][tex]\sf{r = ( \dfrac{41070}{27750})^{ \frac{1}{6} } - 1 }[/tex][tex]\sf{\green{\boxed{\sf{{r ≈6.87\%}}}}}[/tex]
