Question

1. If I invest $1,000 at the start of each year every year for the next four years in an account paying 4% annual interest, how much will I receive at the end of 4 years? (ordinary annuity vs. annuity due)

Answer 1

You can solve it using a table in excel as given below :

Year	Opening Balance (A)	Investment (B)	Interest (C) = (A+B)*4%	Closing Balance (D = A+B+C)
1	-	1,000.00	40.00	1,040.00
2	1,040.00	1,000.00	81.60	2,121.60
3	2,121.60	1,000.00	124.86	3,246.46
4	3,246.46	1,000.00	169.86	4,416.32

First Year Opening Bal =0, Opening Bal in the year 2 = Closing Balance in Year 1 and like wise...

Investment at $1000 is done at start of the year every year.

Since Investment is done at the start of each year, you will earn full year interest @4% on the investment. You will also earn interest on the opening balance (Cumulative amount already in your account).

The Closing Balance at each year end would be the sum of all three - Openeing Bal + Investments done duringthe year + Interest Earned.

Thus the amount you will receive at the end of 4 years = $4416.32 .

You can also solve it using The Future Value function in Financial Calculators and Excel

Where

Rate = 4%

NPER = 4

PMT = -1000 (Cash outflow, investment)

PV = 0

Type = 1, since you make investments at the beginning of the period. You could chose 0, if you make investments at end

Thus Future Value of investments after 4 years = FV(4%,4,-1000,0,1) = $4416,.32