QUESTION 4 (25 MARKS) (UNIT 2) a) Why does money have a time value? Does inflation have anything to do with making a ringgit today wprth more than a ringgit tomorrow? (4 marks) b) Discuss the present value of an annuity due with an example

Qa) Money has time value because we can invest the money today and earn interest on it. This increases the value of the money received today than the money to be received in future.

Yes, inflation does play a role in making ringgit worth more today than tomorrow. This is because inflation decreases the purchasing power of money. Higher the inflation lower will be the value of money and vice versa. So, a dollar is worth more at present than it will be worth tomorrow.

Qb) Annuity due refers to a series of equal payments made at the same interval at the beginning of each period.The first payment is received at the start of the first period and, thereafter, at the start of each subsequent period.The present value of an annuity due uses the basic present value concept for annuities, except that cash flows are discounted to time zero.

For Calculating the PVAD

For this formula, the following values are used:

P = periodic payment

r = rate per period

n = number of periods

The formula used is:

PVAD = P + P [ (1 - (1 + r) ^{- (n - 1)} ) ÷ r ]

For example, an annuity due's interest rate is 5%, you are promised the money at the end of 3 years and the payment is $100 per year.

Using the present value of an annuity due formula:

(100 + 100 [ (1 - (1 + .05) ^{- (3 - 1)} ) ÷ .05 ]

(100 + 100 [1 - (1.05) ^{- 2} ÷ .05 ] = $285.94

The value of $285.94 is the current value of three payments of $100 with 5% interest.

Qc) Using financial calculator to calculate the Future value

Inputs: N= 18

I/y= 10%

Pv= -15,000

Pmt= 0

Fv= compute

We get, future value of the deposit as RM83,398.76

Qd) Using financial calculator to calculate the monthly payment.

Inputs: N= 5 × 12 = 60 ( monthly compounding)

I/y= 6% / 12 = 0.5%

Pv= 0

Fv= 20,000

Pmt= compute

We get, monthly payment as RM 286.66

Qe) Using financial calculator to calculate the future value

Inputs:- N= 10

Pmt= -1,200

I/y= 6%

Pv= 0

Fv= compute

We get , future value of deposit as RM 15,816.95