Question

4.What is the present value of the deferred annuity if the regular payment is P15,000.00 every month, the interest rate is 8% compounded monthly, with an actual payments of 24, and the period of deferral is 12? 5. What is the present value of the deferred annuity if the regular payment is P5,000.00 every year, the interest rate is 5% compounded annually, with an actual payments of 6, and the period of deferral is 12? 6.What is the present value of the deferred annuity if the regular payment is P5,000.00 every month, the interest rate is 1.5% compounded monthly, with an actual payments of 12, and the period of deferral is 2? 7.What is the present value of the deferred annuity if the regular payment is P500.00 every month, the interest rate is 2% compounded monthly, with an actual payments of 60, and the period of deferral is 20? 8. What is the present value of the

Answer 1

Question 4. Solution:

Present value of deferred annuity = Pmt.×[1-(1+i)^-n] / [(1+i)^t ×i ]

Where, i = Interest rate

n = no. of payments and t = period of deferrals

So, present value of deferred annuity = $15,000×[1-(1+0.08/12)^-24] / [(1+0.08/12)¹²× (0.08/12)

   = $306,240.36 (Rounded off)

Note: Here in above calculations, the interest rate is devided by 12 because the monthly compounding exists in the question.

Question 5.

Solution : Present value of deferred annuity = $5,000×[1-(1+0.05)^-6] / [(1+0.05)¹²×0.05]

= $14,131.68 (Rounded off)