Geometric progression(sinking fund)

Question

A person saves $1000 in a bank account at the beginning of each year. The bank offers a return of 12% compounded anually. Determine the total amount after 10years.

My lecturer's answer:

S10=1000(1.12)(1.12^10-1)/1.12-1

I don't understand the intention of him multiplying 1000 with 1.12. isn't a=1000 only? Correct me if I'm wrong. Thank you.

Answer 1

I used this formula and changed "fv" with the new value each year. The formula is fv=p(1+int/c)^(nt).

first value 1120 fv future value

2nd 2374.4 p premium

3rd 3779.33 int

4th 5352.85 c compound

5th 7115.19 n years

6th 9089.01 t times/yr

7th 112999.69

8th 13775.66.

9th 16548.74

10th $19654.58

This formula is set for 1 deposit. you stated that each yr $1000 is deposited.