Question

You will retire 20 years from now, and you think you will need an income of $6,000 per month for 20 years after you retire.

You will begin saving for retirement by saving $700 per month for the next 10 years. How much will you have to save each month in the 10 years after that to have enough to meet your retirement goal?

The interest rate is 9% APR.

Round your answer to the nearest dollar.

Answer 1

Step-1:Calcualtion of present value of after retirement income 20 years from now
Present value	=	Monthly Income	*	Present value of annuity of 1
	=	$             6,000	*	111.145
	=	$       6,66,870
Working:
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.0075)^-240)/0.0075		i	9%/12	=	0.0075
	=	111.144954		n	20*12	=	240
Step-2:Calculation of future value of monthly saving of first 10 years from now at the time of 20 years from now
Future value	=	Monthly saving	*	Future value of annuity of 1	*	Future value of 1
	=	$                 700	*	193.5143	*	2.451357
	=	$       3,32,061
Working:
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.0075)^120)-1)/0.0075		i	9%/12	=	0.0075
	=	193.5142771		n	10*12	=	120
Future value of 1	=	(1+i)^n
	=	(1+0.0075)^120
	=	2.451357078
Step-3:Calculation of per month saving for next 10 years
Total amount needed 20 years from now		$       6,66,870
Less future value of monthly saving for first 10 years		$       3,32,061
Required future value of monthly saving of next 10 years	a	$       3,34,809
Future value of annuity of 1 for 10 years	b	193.5142771
Required monthly saving for next 10 years	c=a/b	$             1,730