April opened a savings account with a deposit of $500. 5% compound interest each year. How much interest will April's deposit earn at the end of 3 years?

Question

One time deposit is 500$...saving account will earn 5% compound intrest...

Answer 1

Because it compounds annually, each year we will add 5% of the amount in the account to what was in the account.  For example after year one we will add 5% of 500$ to the 500$, resulting in 525$.  However the next year we will add 5% of 525$ to the 525$ so 525 + .05(525) which results in $551.25.  Another way of solving this type of problem is realizing that you are essentially taking X and adding .05X to it, which is the same as X+.05X or simplified to 1.05X.  So each year we can just multiply the previous amount in the account by 1.05 (1 + the interest rate).  since we are multiplying this original amount by 1.05 five times, we can write it as an exponential equation  500(1.05)⁵ which is equal to about $638.14 This is also where the formula comes from where A=P(1+r)ⁿ  Amount is equal to Principal times (1+ interest rate) to the number of time periods.