Question

Suppose your parents are helping you invest money to save for the future. They open an account foryou in January with an initial deposit of $200 that is compounded monthly at a rate of 3.6%. From nowon, at the end of each month, you will deposit $200. How much money will be in your account at theend of the year?

Answer 1

Lets go over every month:

First deposit: $200

At the end of january we will have earned the interests of the month

January: $200*(1 + 0.036) = $207.2

For the next month we will have $207.2 plus the new deposit of $200. That will be 407.2. Then, at the end of february, we will earn the interests with this amount.

February: $407.2*(1 + 0.036) = $421.86

We can continue with this logic until the end of the year:

March: ($421.86 + $200)*1.036 = $644.25

April: ($644.25 + $200)*1.036 = $874.643

May: ($874.643 + $200)*1.036 = $1113.33

June: ($1113.33 + $200)*1.036 = $1360.61

July: ($1360.61 + $200)*1.036 = $1616.79

August: ($1616.79 + $200)*1.036 = $1882.2

September: ($1882.2 + $200)*1.036 = $2157.15

October: ($2157.15 + $200)*1.036 = $2442.01

November: ($2442.01 + $200)*1.036 = $2737.13

December: ($2737.13 + $200)*1.036 = $3042.86

At the end of the year, the account will have $3042.86