Question

You are an insurance company and have sold an annuity to a customer.
The annuity pays 240 monthly payments (the same each month) starting 12 months from today.
The monthly paymenst are $500 per month.
If your firm earns 5.00% APR (compounded monthly), on its investments,
how much does it have to invest today to just cover the cost of the annuity?

Answer 1

Investment today is $ 72,075.15

Working:

Investment today	=	Monthly Payment	*	Present value of annuity of 1	*	Present value of 1
	=	$       500.00	*	151.5253	*	0.951328
	=	$ 72,075.15
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.004167)^-240)/0.004167		i	=	5%/12	=	0.004167
	=	151.525313		n			=	240
Present value of 1	=	(1+i)^-n		Where,
	=	(1+0.004167)^-12		i	=	0.004167
	=	0.95132824		n	=	12