athe end of everymonth Elle Deposits $500 into a savings account,with an anual interest rate of 6% compounded?

Question

the end of everymonth Elle Deposits $500 into a savings account,with an anual interest rate of 6% compounded monthly.How much interrest will be earned at the end of 4 years?

Answer 1

Picopico's answer would only work if it was invested and compounded yearly.

Month 1: 500
M2: 500 + M1 (1 + .005) - use .005 because its 6% / 12 months.
M3: 500 + M2(1 + .005)...
out to 48 months.

Now, here's a trick:
The first month's payment has had 47 interest payments on it...the second month's payment has had 46 interest payments, etc.

It can be rewritten as: 500 (1 + .005)^47 + 500 (1 + .005)^46 + 500 (1 + .005)^45...
then: 500 (((1 + .005)^47) + ((1 + .005)^46) + ((1 + .005)^45)...(1+.005)^0))

Any regression of (a^n + a^n-1 + a^n-2...a^0) can be rewritten as:
((a^n+1) - 1)/(a-1)
a = 1 + .005 = 1.005
n = 47

So, you can now write it as: 500 * ((1.005^48)-1/.005)
500 * ((.270489161/.005))
500 * 54.09783222 = $27048.92

Answer 2

year 1: 0.06 times $500 = interest earned year 1
year 2: 0.06 times ($500+interest earned year 1) = interest earned year 2
year 3: .06 times ($500+interest earned year 1+interest earned year 2) = interest earned year 3
Do the same for year 4, then add the interest earned for all four years together.

The tricky part of this question is the compound interest - just remember to add the interest earned each year to the $500 already in the bank.