Question

What is the present value of an annuity of SAR800 received at the end of each year for 12 years? Assume a discount rate of 10%. The first payment will be received one year from today (round your answer to nearest SAR1).

Answer 1

We know the formula for present value of ordinary annuity is

Present value of annuity - P*((1-(1+r)^-n)/r

Where P = Equalised periodic payment

r = rate of interest

n = Number of periods

Given that P = SAR800

r = 10%

n = 12 years

Let us substitute the above values in the formula

Present value of annuity = 800*(1-(1.1)^-12)/0.1

= 800 * (1 - 0.318631)/0.1

= 800 * 6.813692

= 5450.953SAR

= 5451SAR

This can be better tabulated as below

Year	Cash Flows	Discount factor	Present Value
1	800	0.909	727.273
2	800	0.826	661.157
3	800	0.751	601.052
4	800	0.683	546.411
5	800	0.621	496.737
6	800	0.564	451.579
7	800	0.513	410.526
8	800	0.467	373.206
9	800	0.424	339.278
10	800	0.386	308.435
11	800	0.350	280.395
12	800	0.319	254.905