If an insurance company offers you annuity payments of $45,000 per year for the first 12 years of retirement and $52,000 per year for the next 12 years

If an insurance company offers you annuity payments of $45,000 per year for the first 12 years of retirement and $52,000 per year for the next 12 years, what would you be willing to pay for this annuity if you have a required rate of return of 6%? Assume beginning of year payments

Expert Solution

The question is based upon time value of money.
Step-1:Present value of annuity for 12 years

Present value	=	Annuity * Present value of annuity of 1
	=	$ 45,000.00	*	8.886874577
	=	$ 3,99,909.36

Working:

Present value of annuity of 1	=	((1-(1+i)^-n)/i)*(1+i)		Where,
	=	((1-(1+0.06)^-12)/0.06)*(1+0.06)		i	6%
	=	8.886874577		n	12

Step-2:Present value of annuity for next 12 years

Present value	=	Annuity * Present value of annuity of 1*Present value of 1
	=	$ 52,000.00	*	8.886874577	*	0.496969
	=	$ 2,29,658.23

Working:

Present value 1	=	(1+0.06)^-12		Where,
	=	0.496969364		i	6%
				n	12
Step-3:Value of annuity

Value of annuity is the present value of future annuity payments.

So, Value of annuity	=	$ 3,99,909.36	+	$ 2,29,658.23
	=	$ 6,29,567.58

ekkarill92 answered 1 year ago

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