Question

Your local bank is offering a new type of retirement savings account. An initial deposit is made to the account when it is opened. This money and any accumulated interest must be left in the account for 27 years. No additional deposits can be made. On the day the account is opened and on each annual anniversary of the initial deposit, the account balance is reviewed and the following terms apply:

If the account balance is less than or equal to $20,000, interest for the next annual period is 7%/year compounded annually.

If the account balance is greater than $20,000 but less than or equal to $40,000, interest for the next annual period is 10%/year compounded quarterly.

If the account balance is greater than $40,000, interest for the next annual period is 12%/year compounded monthly.

You decide to open an account under these terms today with $10,800. How much money will you withdraw when the account is closed 27 years from today?

Answer 1

10% compounded quarterly =(1+0.1/4)^4-1=10.38% eeffective annual interest rate

12% compounded monthly =(1+0.12/12)^12-1=12.68% effective interest rate

Year	Deposit Amount	Total Balance for Interest application =P	Annual Interest appliacble =i	Year end Compounded balance =P*(1+i)
1	$                   10,800	$                   10,800	7%	$               11,556
2		$                   11,556	7%	$               12,365
3		$                   12,365	7%	$               13,230
4		$                   13,230	7%	$               14,157
5		$                   14,157	7%	$               15,148
6		$                   15,148	7%	$               16,208
7		$                   16,208	7%	$               17,342
8		$                   17,342	7%	$               18,556
9		$                   18,556	7%	$               19,855
10		$                   19,855	7%	$               21,245
11		$                   21,245	10.38%	$               23,450
12		$                   23,450	10.38%	$               25,885
13		$                   25,885	10.38%	$               28,571
14		$                   28,571	10.38%	$               31,537
15		$                   31,537	10.38%	$               34,811
16		$                   34,811	10.38%	$               38,424
17		$                   38,424	10.38%	$               42,413
18		$                   42,413	12.68%	$               47,790
19		$                   47,790	12.68%	$               53,850
20		$                   53,850	12.68%	$               60,678
21		$                   60,678	12.68%	$               68,373
22		$                   68,373	12.68%	$               77,042
23		$                   77,042	12.68%	$               86,811
24		$                   86,811	12.68%	$               97,819
25		$                   97,819	12.68%	$            110,222
26		$                110,222	12.68%	$            124,198
27		$                124,198	12.68%	$            139,947

So I can withdraw $139,947 after 27 Years from today.