Question

Mr. Lyon, would like to retire in 27 years. He would like to accumulate $1,500,000 at the time of retirement to live a contented life. He would like set aside equal amount each month to achieve his goal. What is the monthly amount he should save if he can invest them at an interest rate of 11.2% [Annual rate]. [Assume monthly compounding]

	$725.88
	$532.24
	$442.38
	$831.57

Answer 1

Given,

Years before retirement = 27 years

Future value = $1500000

Interest rate = 11.2% or 0.112

Solution :-

No. of months (n) = 27 years x 12 months = 324

Monthly interest rate (r) = 0.112 12 months = 0.0093333333

Let monthly savings be 'M'

Future value = M/r x [(1 + r)ⁿ - 1]

$1500000 = M/0.0093333333 x [(1 + 0.0093333333)³²⁴ - 1]

$1500000 x 0.0093333333 = M x [(1.0093333333)³²⁴ - 1]

$13999.99995 = M x [20.28689654 - 1]

$13999.99995 = M x 19.28689654

$13999.99995 19.28689654 = M

$725.88 = M

Thus, he should save $725.88 monthly.