Question

You plan to buy a house in 18 months. The cost of the house at that time will be $300,000 . How much do you have to invest each month, starting next month, for 12 months to exactly pay for the house if you r investments earn 2.00% APR (compounded monthly)?

$22,675 $25,261 $24,525 $23,582 $24,290

Answer 1

Cost of house in 18 months = $300,000
Annual interest rate = 2.00%
Monthly interest rate = 2.00% / 12
Monthly interest rate = 0.1667%
Number of deposits = 12

Let monthly deposits be $x

$x*1.001667^17 + $x*1.001667^16 + … + $x*1.001667^7 + $x*1.001667^6 = $300,000
$x * 1.001667^6 * (1.001667^12 - 1) / 0.001667 = $300,000
$x * 12.232272 = $300,000
$x = $24,525

Therefore monthly deposits are $24,525