Question

Subject INTRODUCTION TO FINANCIAL MANAGEMENT

1. Find the future value of an ordinary annuity of RM1,500 each year for 12 years, deposited at 4.50 per cent. WITH CALCULATION.

2. Estimate how much is the present value of an ordinary annuity of RM1,550 each year for four years, assuming an opportunity cost of 3.50 per cent. WITH CALCULATION.

3.You have been awarded a bonus for your outstanding work. Your employer offers you a choice of a lump-sum of RM6,500 today, or an annuity of RM1,700 a year for the next five years. Decide which option you should choose if your opportunity cost is 8.00 per cent. WITH CALCULATION

4. Solve how many years do you need to accumulate RM8,500 if you save RM6,000 now at 5.00 per cent in saving account at ANZ Bank. WITH CALCULATION

Answer 1

1. Computation of Future value of ordinary annuity

The formula for finding future value of an ordinary annity is:

FV = P ( [(1+r)ⁿ - 1] / r )

where:

P = Periodic payments = 1500

r = Rate of interest = 4.5% ie, 0.045

n = number of periods = 12

= 1500 ((1.045¹² - 1) / 0.045)

= 1500 ((1.69588 - 1) / 0.045)

= 1500 * 15.464

= 231960

2. Computation of Present value of ordinary annuity

The formula for finding present value of an ordinary annity is:

PV = P ( [ 1 - (1+r)^-n] / r )

= 1550 ([ 1 - 1.035^-4] / 0.035)

= 1550 ([1 - 0.87144] / 0.035)

= 1550 * 3.67314

= 5693.27

3. Choosing between Lumpsum or Annuity

The decision would be to accept the Lumpsum amount or Present value of Annuity whichever offers higher amount.

Lumpsum amount = 6500

The formula for computing Present value of annuity

PV = P [(1 - (1+r)^-n) / r]

P = Periodic payments = 1700

r = Rate of interest = 8% ie, 0.08

n = number of periods = 5

= 1700 [(1 - 1.08^-5 ) / 0.08]

= 1700 * [(1 - 0.6805) / 0.08]

= 1700 * 3.99271

= 6787.61

The present value of annuity $6787 is higher than the lumpsum amount which is $6500. Therefore, it is better to choose the annuity that offers $1700 for the next 5 years.

4. Computation of number of years

You have to find the number of years it takes for $6000 to become $8500 when the interest rate is 5%

(Assume that interest is compounded annually)

This can be solved by using the following formula

P (1 + r )ⁿ = Final amount

where, P = Principal amount, r = rate of interest, n = number of years

Find 'n' using trial and error method. The year which gives the final amount $8500 will be the answer

6000 (1 + 0.05)ⁿ = 8500

when n = 5,   6000 (1 + 0.05)⁵ = 7657.68

when n = 6, 6000 (1 + 0.05)⁶ =  8040.57

when n = 7,   6000 (1 + 0.05)⁷ =  8442.60 (So we can assume that n is near to 7.1 years)

when n = 7.1,  6000 (1 + 0.05)^7.1 = 8484

when n = 7.14, 6000 (1 + 0.05)^7.14 = 8500

Therefore number of years is 7.14 years.