Question

You plan to work for Strickland Corporation for 12 years after graduation and after that want to 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 grandmother just gave you a $20,000 graduation gift that 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? Select the correct answer. a. $263,721 b. $263,746 c. $263,758 d. $263,709 e. $263,734

Please show all work or calculator steps! Thank you!

Answer 1

Answer: We have to calculate the future value of all the Investments done at the end of 12th year.

So an Investment done in the starting will get compounded for 12 years

Investment done at the end of 1st year will get compounded at the end of 1st year will get compounded for 11 years

And Similarly for rest of the Investments done

Only the last investment of 15000 at the end of 12 th year will not get a chance to get compounded

Compounding formula = Amount*(1+ rate)^ (no of years)

rate = 9% given

A matrix table will form like this where previous year amount is multiplied by (1+ rate ) to get next year amount

Year	0	1	2	3	4	5	6	7	8	9	10	11	12
0 Amount* (1+ 0.09)	20000	21800	23762	25900.58	28231.63	30772.48	33542	36560.78	39851.25	43437.87	47347.27	51608.53	56253.3
1		7500	8175	8910.75	9712.718	10586.86	11539.68	12578.25	13710.29	14944.22	16289.2	17755.23	19353.2
2			7500	8175	8910.75	9712.718	10586.86	11539.68	12578.25	13710.29	14944.22	16289.2	17755.23
3				7500	8175	8910.75	9712.718	10586.86	11539.68	12578.25	13710.29	14944.22	16289.2
4					7500	8175	8910.75	9712.718	10586.86	11539.68	12578.25	13710.29	14944.22
5						7500	8175	8910.75	9712.718	10586.86	11539.68	12578.25	13710.29
6							7500	8175	8910.75	9712.718	10586.86	11539.68	12578.25
7								15000	16350	17821.5	19425.44	21173.72	23079.36
8									15000	16350	17821.5	19425.44	21173.72
9										15000	16350	17821.5	19425.44
10											15000	16350	17821.5
11												15000	16350
12													15000
Sum at the end of 12th year													263733.7

Total Value is coming out to be $263734. So option E is the answer.