Who is asking: Student
Level: Secondary
Question:
this is the problem:
suppose u have $25,000 to invest and the interest rate at your bank is 11%.
1) how much money would you have at the end of EACH of the first four years?
1) i already kno that the first year w/ interest is $27,750 but how do i get the 2nd? 3rd? 4th? years?
2)How much money would you have in 10 years?
2) do i just add up all the years?
3) find an equation for how much money you would have after n years?
3) will the equation be linear or exponental or neither? or what?
can u please try to explain this, i kno it has to do w/ geometric sequences, so if u could incorporate that into these problems that would be great, thanks


Hi,
If the bank says "the interest rate is 11% per year" they mean that it is 11% per year, compounded yearly. That is, at the end of each year you get the principle (what you started the year with) plus 11% of the principle. Thus, as you noted, at the end of the first year you get
$25,000 plus 11% of $25,000
which is
$25,000 + ^{11}/_{100} $25,000
= $25,000 + 0.11 $25,000
= 1.11
$25,000
= $27,750
Now, at the beginning of the second year you have a principle of $27,750 so at the end of the second year you have
$27,750 + ^{11}/_{100} $27,750
= 1.11 $27,750
= 1.11 1.11 $25,000
= 1.11^{2} $25,000
= $30,802.50
This is the principle at the beginning of the third year, so at the end of the third year you have
1.11^{2} $25,000 + ^{11}/_{100} (1.11^{2} $25,000)
= 1.11^{3} $25,000
Does this help?
Penny

