if you spend $2,548 a year, how much would you save after 5 years if every year you put that money into a savings account that earned 5% annual interest. 25 years? 50 years?
+7 5%+100=105%=105/100=1.05
**without following years:
[saving - spending]*years*1.05^years=
[2548*(1.05) -2548]5*1.05^5=812.99
[2548*(1.05) -2548]25*1.05^25=
[2548*(1.05) -2548]50*1.05^50
+7 5%+100=105%=105/100=1.05
**without following years:
[saving - spending]*years*1.05^years=
[2548*(1.05) -2548]5*1.05^5=812.99
[2548*(1.05) -2548]25*1.05^25=
[2548*(1.05) -2548]50*1.05^50
+118608 okay, Say you put the money in the bank at the END of each yeaar.
How much will you have at the END of 5 years.
Ok
the first deposit of $2548 will be earning 5% pa interest for 4 years
This is how much it will grow to
$${\mathtt{2\,548}}{\mathtt{\,\times\,}}{\left({\mathtt{1.05}}\right)}^{{\mathtt{4}}} = {\mathtt{3\,097.109\: \!925}}$$
that is $3097.10
the second deposit of $2548 will be earning 5% pa interest for 3 years
This is how much it will grow to
$${\mathtt{2\,548}}{\mathtt{\,\times\,}}{\left({\mathtt{1.05}}\right)}^{{\mathtt{3}}} = {\mathtt{2\,949.628\: \!5}}$$
that is $2949.63
the third deposit of $2548 will be earning 5% pa interest for 2 years
This is how much it will grow to
$${\mathtt{2\,548}}{\mathtt{\,\times\,}}{\left({\mathtt{1.05}}\right)}^{{\mathtt{2}}} = {\mathtt{2\,809.17}}$$
that is $2809.17
the forth deposit of $2548 will be earning 5% pa interest for 1 years
This is how much it will grow to
$${\mathtt{2\,548}}{\mathtt{\,\times\,}}\left({\mathtt{1.05}}\right) = {\mathtt{2\,675.4}}$$
that is $2675.40
the fith deposit of $2548 will be earning 5% pa interest for 0 years (you only just now depositied it
So it will still be worth $2548
NOW add all those together and you will see how much your deposits will grow to after 5 years.
$${\mathtt{3\,097.1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2\,949.63}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2\,809.17}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2\,675.4}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2\,548}} = {\mathtt{14\,079.3}}$$
+128631 I believe we have an annuity here...the "formula" for the accumulated amount after "n" years is given by
A = C [ (1 + i )n - 1 ] / i where C is the cash flow per period, i is the interest rate per period, and n is the number of periods - (in this case, years)
I'll do the first one for you.....and you can "plug and play" to arrive at the other two answers
for the accumulated amount after 5 years, we have
A = 2548 [ (1 + .05)5 - 1] / .05 = $14, 079. 31
+118608 Now if you want 25 years of 50 years you probably need to develope a formula or use one that someone else has already developed.
It it the future value of an annuity problem.
Use future value of an ordinary annuity with n=25 and 50 respectively
