Question

Please answer ALL questions or save for another person who will.

1. If you invested money into a savings account earning 6% annual interest compounded semiannually (m=2), how many years would it take to double your money?
2. After inheriting a large sum of money you are looking to purchase a certificate of deposit (CD) at a local bank. Bank A is willing to give you an interest rate of 3.19% compounded monthly. Bank B is willing to give you an interest rate of 3.21% compounded semi-annually.
    Determine which bank you should put your money and explain why you arrived at the decision.

3.   The bank is offering a Savings CD account were you would earn 5% interest compounded quarterly if you left the money in the account for 18 years. How much money would you need to invest in the account if you want the final balance on the account to be $100,000 at the end of the 18 years?
      

Answer 1

1. The number of years is computed as follows:

Future value = Present value x (1 + r)ⁿ

2 = 1 x (1 + 0.06 / 2)ⁿ (r has been divided by 2, since the interest is compounded semi annually)

2 = 1.03ⁿ

Take log on both sides, we shall get:

log 2 = n log 1.03

0.693147181 = n x 0.029558802

n = 0.693147181 / 0.029558802

n = 23.44977227 years

Now, since the interest is compounded semi annually, hence n shall be divided by 2:

= 23.44977227 years x 2

= 46.90 years Approximately

2. EAR of Bank A is computed as follows:

= (1 + r / m)^m - 1

= (1 + 0.0319 / 12)¹² - 1

= 3.237056227%

EAR of Bank B is computed as follows:

= (1 + r / m)^m - 1

= (1 + 0.0321 / 2)² - 1

= 3.23576025%

Since the EAR of Bank A is greater than the EAR of Bank B, hence Bank A shall be chosen

3. The amount is computed as follows:

Present value = Future value / (1 + r)ⁿ

= $ 100,000 / (1 + 0.05 / 4) ^{18 x 4}

= $ 100,000 / 1.0125⁷²

= $ 40,884.41

Feel free to ask in case of any query relating to this question