Answer to Question #207160 in Financial Math for Waleed

Question

a capital of 500 dollars earns 150 dollars of interest in 6 years. What was the 

interest rate if compound interest is used? What if simple interest is used?

Answer 1

Simple Interest ;

$150=\frac {500×6×r}{100}$

$r=\frac {150×100}{500×6}$

r=5%

Compound Interest ;

$C. I=P [(1 +\frac {r} {100} )^{n} - 1]$

$150=500[(1+\frac {r} {100})^6-1]$

$\frac {150}{500}+1=(1+\frac {r} {100})^6$

$\frac {650} {500}=(1+\frac {r} {100})^6$

$\frac {13}{10} =(1+\frac {r} {100})^6$

$(\frac {13}{10}) ^{\frac {1} {6}}=(1+\frac {r} {100})$

$r=[(\frac {13}{10}) ^{\frac {1} {6}} - 1]×100$

r=4.47%