Finding simple interest with geometric series

Question

Ms. Montgomery invested $1600 at 12% simple interest at the beginning of each year for a period of ten years. Find the total accumulated value of all the investments at the end of the 10-year period.

Answer 1

Your question has a problem.

Simple interest will NOT involve a geometric series.

The amount invested in the first year with SIMPLE interest for 10 years amounts to 1600 + 1600*.12*10=3520

 

Over the 10 years she will have 1600 invested for (10+...+1) years (Note: an arithmetic series!)

That  is 1600*[(10*11)/2]*.12 interest in 10 years = 10560 plus the investment of 1600*10 each of the 10 years, i.e. 16000

Therefore at the end of year 10 she will have 16000 + 10560 = 26560.