The answer I got for this isn't making sense to me.

Question

A person deposits $5000 into a investment account at the end of each year for 10 years. The account earns 4% interest annually. What is the future value of the annuity after the 10th deposit? 

Answer 1

The formula you need is

 

Total = Initial* (1+interest)^time + deposit * ( (1+interest)^time - 1)/ interest

 

Let's explain this. Total is the total money you end up with at the end of all the time. Initial is the money that the account starts with. Interest is the percent interest (note that this formula works only for interest annually and that is not compounded in any way). Deposit is the amount you put into the account each year. Time is the years you do this for. 

 

For this problem, we have

 

Initial= 5000

Interest = 4%= 0.04

Deposit= 5000

Time = 10

 

So we have

 

Total = 5000*(1+0.04)^(10) + 5000* ( (1+0.04)^(10) - 1)/ 0.04

        = 5000*(1.04)^(10) + 5000*( (1.04)^(10) - 1)/ 0.04

        = 7401.22 + 5000* (1.448024 - 1)/0.04

        = 7401.22 + 5000 * (.448024/.04)

        = 7401.22 + 5000 * 12.0061

        = 7401.22 + 60,030.50

        = 67,431.80

 

So the total amount in the end of the account is $67,431.80.