Question

Sumeet has a 13 year annuity that pays at the end of each year. The first payment is $2000 and the payments grow by R = 5% per year. Interest rates are r = 6% annually. a) How much is Sumeet's annuity worth? Consider the following two options: Option A: An annuity with the same number of payments, only each payment is twice the payment of his current annuity. Option B: An annuity where the initial payment is the same as his current annuity, the growth rate of the payments is the same, but he gets twice as many payments. b) Without doing the computation, which do you think he would prefer? (No marks for this question, so feel free to take your best guess.) c) Calculate the value of option A. d) Calculate the value of option B. e) What would your answer be if r = R?

Answer 1

Present value of growing annuity is calculated using the formula: (P/(r-g))*(1-((1+g)/(1+r))^n), where P is first payment, r is interest rate, g is growth rate and n is number of years.

a).

On Substituting, we get,

Sumeet's annuity worth= 2000/(6%-5%)*(1-(1.05/1.06)^13)= $23186.82

b).

Option A would be more preferable, because eventhough the number of payments are increased in Option B, their present value will be decreased when discounted.

c).

Given that each payment is twice the payments of current annuity.

So, Value of Option A= 4000/(6%-5%)*(1-(1.05/1.06)^13)= $46373.64

d).

Given that payments are twice. So, the annuity is for 26 years.

So, Value of Option B= 2000/(6%-5%)*(1-(1.05/1.06)^26)= $43685.50

e).

If r=R, which means interest rate and payment growth rate are same, Option A and Option B would be same. The value when th payments are doubled and the value when number of payments are doubled, will be equal.