Question 535620
As I understand, no interest is added daily, but after half a year 6% interest is added. That would be
{{{2000*0.06=120}}}
The total balance would then be
{{{2000+2000*0.06=2000*1.06}}}
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}}}
That happens twice per year, or {{{2n}}} times in {{{n}}} years.
If after {{{n}}} years the balance is 3000 more
{{{2000*1.06^(2n)=5000}}}
{{{log((2000*1.06^(2n)))=log((5000))}}}-->{{{log((2000))+2nlog(1.06)=log((5000))}}}
{{{2nlog(1.06)=log((5000))-log((2000))=log((5000/2000))=log((2.5))}}}
{{{n=log((2.5))/(2log(1.06))=7.86}}}
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.
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.