Question

Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the first month, 4 at the end of the second month, and for each month thereafter the payment increases by 2. The annual nominal interest rate is 9% convertible quarterly.CALCULATE X

Answer 1

Nominal interest rate is = 9% converible quaterly

we need to find monthy effective interest rate

0.09

i = 0.00744 or 0.75% approximately

i can also be taken as = 0.09/12

now PV of annuity will be the market price i.e x

6 60 *2 ---------------------a

Multiply equation by \frac{1}{1+i} both sides

6 60 2 PV ---------------b

Subtract equation b from a

60 2 PV (1 1+i (1+2)1 (1+2)2 (1+2)3 (1+2)60 (1+961

60 2 PV( 1 +i

on putting i = 0.00744

PV = 2733.88 approximately

X = 2733.88

Explanation: