Question

There are four banks: A, B, C and D:

• Bank A offers an effective annual rate of 4.02%.

• Bank B offers a nominal annual interest rate of 4 % compounded semiannually.

• Bank Coffers a nominal annual discount rate of 3.96% compounded monthly.

• Bank D offers a nominal annual interest rate of 3.98% compounded continuously.

(a) According to this ir rmation, where would you prefer to open a savings account? Justify your answer. [4 marks]

(b) If you have saved a certain amount of money and deposit it in the bank of

your choice, how lo will it take you to triple your savings?[3 marks]

( c) Find the equivalent nominal annual discount rate compounded monthly for

Bank D.

Answer 1

a. in would invest in a Bank which offers highest effective annual interest rate

Bank A Effective Annual Interest = 4.02%

Bank B Effective Annual Interest = (1 + Interest per Semi Annual )^Periods per years -1 = 1.02^2 - 1 = 4.04%

Bank C Effective Annual Interest = (1 + Interest per Month)^Periods per years -1 = 1.0033^12 - 1 = 4.03%

Bank D Effective Annual Interest = EXP(Rate * Time)-1 = EXP(3.98%)-1 = 1.040603 = 4.06%

I would invest in bank D as it offers highest effective annual interest Rate

b. Years it will take to triple Investment in Bank D

Future Value = Investment * EXP(Rate*Time)

3 = 1 * EXP(3.98%*Time)

EXP(0.0398*time) = 3

Time Required = 27.60 Years (Calculated using Goal Seek Function in Excel)

c. equivalent nominal annual discount rate compounded monthly

(1 + Interest per month)^12 - 1 = 4.06%

(1 + Interest per month)^12 = 104.06%

1 + Interest per month = 100.3322%

Interest per month = 0.3322%

equivalent nominal annual discount rate compounded monthly =interest per month * 12 = 0.3322%*12 = 3.9866%

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