Question

Assume you are planning to invest $5,558 each year for six years and will earn 7 percent per year. Determine the future value of this annuity due problem if your first $5,558 is invested now. (Round answer to 2 decimal places, e.g., 1,220.25.)

Answer 1

Amount invested in the beginning of each year = $5,558

Interest received each year = 7 %

Each year interest will be received on the total of that years deposit plus amount accumulated from previous years deposits and interest. For example,

2nd years interest will be calculated on the amount ( total of 2nd years deposit i.e $5,558 and amount accumulated from 1st years deposit and interest i.e $ 5947.06

= 7 % of (5,558 + 5947.06)

Interest received in 2nd years= $ 805.3542

Like this, interest will be calculated for each year.

Amount accumulated at each year's end will be total of total deposit accumulated from last year plus deposit this year + interest received in this year

For example,

Amount accumulated at end of 2nd year will be = Amount accumulated from 1st year + Deposit of 2nd year + Interest received in 2nd year

= 5947.06 + 5558 + 805.3542

= $ 12310.4142

Like this, it will be calculated for each year

This is shown in table below-

Year	Deposited at beginning of each year ($)	Interest Received in current year $	Total Deposit (in $) = total deposit accumulated from last year + deposit this year + interest received
1	5558	389.06	5947.06
2	5558	805.3542	12310.4142
3	5558	1250.788994	19119.20319
4	5558	1727.404224	26404.60742
5	5558	2237.382519	34199.98994
6	5558	2783.059296	42541.04923

Future value of annuity = $ 42541.04923

= 42541.05 $ (approx)

Hope it helps!