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 20 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:

1. If the account balance is less than or equal to $20,000, interest for the next annual period is 7%/year compounded annually.
2. 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.
3. If the account balance is greater than $40,000, interest for the next annual period is 12%/year compounded monthly.
4. 
   
5. You decide to open an account under these terms today with $8,000. How much money will you withdraw when the account is closed 20 years from today?

Answer 1

The initial Amount that is invested = $8000.

The formula for total amount calculated is A=P(1+r/100)^t.

A=total amount

P=Initial investment

t=time period

r=rate of interest.

condition 1 is applied at the start of the account.

hence, the amount calculated for the following years when the amount is less than 20,000 at the rate of 7%.

to find when the amount surpasses 20,000.

substitute the variables with values in the formula

consider A=20000

P=8000

T=t

R=7%

20000<=8000(1+7/100)^t

2.5<=(107/100)^t.

on solving the above equation the value of t will be 13.8.

Hence after 14 years the value of amount will surpass 20000.

which will be equal to by using the above formula 20,628.273.

from the 15 year condition 2 will apply.

Using the above formula check if the amount will surpass 40000 at the rate of 10% annually.

A=20,268.273(1+10/100)^6

A=$36544.244

Now you decide to open the account at the end of 20 years the amount of money you withdraw is $36544.244