Algebra.Com's Answer #754839 by ankor@dixie-net.com(22740)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
A bank pays 12% per annum on its savings accounts.
\n" );
document.write( " At the end of every three years, a 2% bonus is paid on the balance at that time. Find the annual effective rate of interest earned by an investor if the deposit is withdrawn
\n" );
document.write( ":
\n" );
document.write( "(a) 3 yrs
\n" );
document.write( "Let just use $100 and find the accumulated amt after 3 yrs,
\n" );
document.write( " annual, so it's pretty simple
\n" );
document.write( "A = 100(1+.12)^3
\n" );
document.write( "A = 100*1.4049
\n" );
document.write( "A = $140.49
\n" );
document.write( "With the 2% bonus: 140.49 * 1.02 = 143.30
\n" );
document.write( ":
\n" );
document.write( "Use this to find the effective interest rate (r)
\n" );
document.write( "100*(1+r)^3 = 143.30
\n" );
document.write( "(1+r)^3 = 143.30/100
\n" );
document.write( "(1+r)^3 = 1.433
\n" );
document.write( "Using common logs
\n" );
document.write( "log((1+r)^3) = log(1.433)
\n" );
document.write( "log equiv of exponents. find the log of 1.433
\n" );
document.write( "3*log(1+r) = .156246
\n" );
document.write( "log(1+r) = .156246/3
\n" );
document.write( "log(1+r) = .05208
\n" );
document.write( "Find the antilog of both sides
\n" );
document.write( "1 + r = 1.1274
\n" );
document.write( "r = 1.1274 - 1
\n" );
document.write( "r = .1274 or 12.74% is the effective rate after 3 years with the bonus
\n" );
document.write( ":
\n" );
document.write( "(b) 4 years. Essentially the same procedure
\n" );
document.write( "One more year with the accumulate amt of 143.30 at 12%
\n" );
document.write( "1.12(143.30) = $160.49 after 4 yrs, find the new r with this amt
\n" );
document.write( "100(1+r)^4 = 160.49
\n" );
document.write( "(1+r)^4 = 160.49/100
\n" );
document.write( "log((1+r)^4) = log(1.6049)
\n" );
document.write( "log(1+r) = .20544/4
\n" );
document.write( "log(1+r) = .05136
\n" );
document.write( "Antilog
\n" );
document.write( "1 + r = 1.1255
\n" );
document.write( "r = .1255 or 12.55% is effective rate after 4 yrs
\n" );
document.write( ";
\n" );
document.write( "Hey, did this make sense to you, should I have been more step-by-step in the 2nd part? CK \n" );
document.write( " |