Question

After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12). The first deposit will be made a year from today. In addition, your grandfather just gave you a $37,500 graduation gift which you will deposit immediately (t = 0). If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?

Answer 1

interest (r) = 9 %

period = 12 years

if we deposit an amount today it will be compounded for the 12 years , if deposit after 1 year it will be compounded for 11 years , last deposit we made after 12 years , so last deposit compounded for zero periods.

Future value factor = (1+r)^n

r - rate of interest = 9 %

n - no. of compounding periods

year	Bal Period of compounding	CF	FVF @9%	FV of CFs
0	12	$ 37,500.00	2.8127	$ 105,474.93
1	11	$    7,500.00	2.5804	$    19,353.20
2	10	$    7,500.00	2.3674	$    17,755.23
3	9	$    7,500.00	2.1719	$    16,289.20
4	8	$    7,500.00	1.9926	$    14,944.22
5	7	$    7,500.00	1.8280	$    13,710.29
6	6	$    7,500.00	1.6771	$    12,578.25
7	5	$ 15,000.00	1.5386	$    23,079.36
8	4	$ 15,000.00	1.4116	$    21,173.72
9	3	$ 15,000.00	1.2950	$    19,425.44
10	2	$ 15,000.00	1.1881	$    17,821.50
11	1	$ 15,000.00	1.0900	$    16,350.00
12	0	$ 15,000.00	1.0000	$    15,000.00
	Balance after 12 years from now			$ 312,955.34

Amount we have at the time we start our business =  $ 312,955.34