Question

Helena is considering investing in an annuity being offered by Akyab Investments Ltd. The annuity will pay her $5,000 per half year for 10 years. Helena is trying to work out how much this annuity is worth. She thinks she should receive a return equivalent to a nominal interest rate of 3.65% per annum, compounding daily. What is the value of this annuity to Helena?

Answer 1

In this case we will have to calculate annual effective interest rate and then calculate monthly payment
Effective annual rate	(1+(r/n)^n)-1)
interest rate is r and frequency of compounding is n
Effective annual rate	(1+(3.65%/365)^365)-1)
Effective annual rate	1.037172-1
Effective annual rate	3.72%
Semi-annual interest rate	3.72%/2
Semi-annual interest rate	1.86%
Present value of annuity	Annuity amount*(1-((1+r)^-n)/r)
interest rate is r and number of payments is n
No of payments	20	10*2
Present value of annuity	5000*(1-(1.0186^-20))/0.0186
Present value of annuity	5000*16.57674
Present value of annuity	$82,883.68
In terms of present value the value of annuity is $82,883.68