H6w to calculate the amount you should invest every month.

Question

On January 1, 2013, you are considering the purchase of a property on January 1, 2015. You expect that the purchase price would be $800,000 and a bank would provide a mortgage loan at that time for 80% of the purchase price. The other costs such as stamp duty and agent commission would be $40,000. In order to accumulate the necessary funds for meeting the down payment and other costs, you plan to invest a constant amount at the beginning of each month starting on January 1, 2013 with the last investment on December 1, 2014. This investment will provide an annual return of 6%.

Calculate the amount you should invest every month to accumulate the down payment and the other costs.

Answer 1

80% of the $800,000 purchase price=$640,000.

The down payment is 20% of the purchase price=$160,000.

Add to this expenses of $40,000=$200,000.

This would need to be the return on the investment between 1 Jan 2013 and 1 Jan 2015 (24 months).

The annual investment rate is 6%, so the monthly rate is 6/12=½% or 0.005.

The first payment accumulates 24 months' interest compounded monthly=1.005²⁴m, the second payment accumulates 23 months' interest, the third payment 22 months' interest and so on. The last payment on 1 Dec 2014 grows to 1.005m by 1 Jan 2015.

When we add all these together we get:

m(1.005²⁴+1.005²³+1.005²²+...+1.005)=1.005m(1.005²⁴-1)/0.005=200000 (sum of geometric series),

m=1000/(1.005(1.005²⁴-1))=$7,825, the monthly payment.