document.write( "Question 535620: In how may years is required for ₱ 2,000.00 to increase by ₱ 3,000 if interest is 12% compounded semi - annually? \n" ); document.write( "

Algebra.Com's Answer #351966 by KMST(5328) $\"\"$ $\"About$

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As I understand, no interest is added daily, but after half a year 6% interest is added. That would be
\n" ); document.write( " $\"2000%2A0.06=120\"$
\n" ); document.write( "The total balance would then be
\n" ); document.write( " $\"2000%2B2000%2A0.06=2000%2A1.06\"$
\n" ); document.write( "If the same thing happens in every half-year period, the balance is the same in between, but every six months interest is added, and the previous balance gets multiplied by $\"1.06\"$
\n" ); document.write( "That happens twice per year, or $\"2n\"$ times in $\"n\"$ years.
\n" ); document.write( "If after $\"n\"$ years the balance is 3000 more
\n" ); document.write( " $\"2000%2A1.06%5E%282n%29=5000\"$
\n" ); document.write( " $\"log%28%282000%2A1.06%5E%282n%29%29%29=log%28%285000%29%29\"$ --> $\"log%28%282000%29%29%2B2nlog%281.06%29=log%28%285000%29%29\"$
\n" ); document.write( "

\n" ); document.write( " $\"n=log%28%282.5%29%29%2F%282log%281.06%29%29=7.86\"$
\n" ); document.write( "So, the 15th time interest is added, 7.5 years after deposit, the balance would have increased by 2793, to 4793. The next time interest is added will be 8 years after deposit, making the balance reach 5,080.70, increased by 3,080.70. You would need 8 years to reach the target balance, and then you would have exceeded it a bit.
\n" ); document.write( "If they kept adding interest to the balance daily (or even continuously), but only compounded semi-annually, then a 5000 balance would be reached at about 7.86 years, and you would not need to wait for the whole 8 years. \n" ); document.write( "

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