Question

rief Exercise G-02 For each of the following cases, indicate (a) to what interest rate columns and (b) what number of periods you would refer to in looking up the future value factor. (1) In Table 1 (future value of 1): Annual Rate Number of Years Invested Compounded Case A 4% 3 Annually Case B 10% 5 Semiannually (a) (b) Case A enter percentages rounded to 2 decimal places for annually compounded interest % enter a number of periods for annually compounded interest periods Case B enter percentages rounded to 2 decimal places for semiannually compounded interest % enter a number of periods for semiannually compounded interest periods (2) In Table 2 (future value of an annuity of 1): Annual Rate Number of Years Invested Compounded Case A 6% 12 Annually Case B 6% 6 Semiannually (a) (b) Case A enter percentages rounded to 2 decimal places for annually compounded interest % enter a number of periods for annually compounded interest periods Case B enter percentages rounded to 2 decimal places for semiannually compounded interest % enter a number of periods for semiannually compounded interest periods

Answer 1

Ans.1. Future value of 1 table:

	Annual rate	Number of years invested	Compounded
Case A	4%	3	Annually
Case B	10%	5	Semi-annually

Case A : Here, interest rate is 4%, compounded annually for 3 years, so, in future value of 1 table, 4% interest column will be referred and number of periods = 3 will be referred.

Case B: Annual rate is 10%, but compounding is semi-annually,so, interest rate per period = 10%/2 = 5%

Further, number of periods will be 5 years * 2 periods per year (since semi-annual compounding), So, 10 periods.

Hence, in the future value of 1 table, 5% interest column will be referred to and number of periods = 10 will be referred.

Ans.2. Future value of an annuity of 1 table:

	Annual rate	Number of years invested	Compounded
Case A	6%	12	Annually
Case B	6%	6	Semi-annually

Case A: Annuity is at 6% annual rate compounded annually for 12 years, so interest rate = 6% and number of periods = 12. So, interest rate = 6% and number of periods = 12 will be referred to in the future value of 1 table.

Case B: Annuity is at 6% annual rate compounded semi-annually, so interest rate per period will be 6%/2 = 3%.

Number of years = 6 with two periods per year. So, number of interest periods = 6*2 = 12

So, in the future value of annuity of 1 table, 3% interest rate with 12 number of periods will be referred to.