Question

MR GREG WANTS TO PURCHASE HIS DREAM HOUSE WHICH WILL COST 600000 IN 15 YEARS. HE IS GOING TO PUT 40000 EACH YEAR FOR TEN YEARS TOWARDS THIS. AT WHAT INTEREST RATE MUST HE INVEST HIS MONEY TO ACHIEVE HIS GOAL.

SOLVE THE QUESTION AND DRAW THE CASH FLOW DIAGRAM

Answer 1

This question deals with the concept of time value of money. For each year, we can see that at the end of time period, what the amount will be equal to. Let rate of interest be r.

For year 1:
Cash outflow = 40,000(1+r)^15
For year 2:
Cash outflow = 40,000(1+r)^14 /because the money now remains in the bank for 14 years
For year 3:
Cash outflow = 40,000(1+r)^13 /time period reduces every year
For year 4:
Cash outflow = 40,000(1+r)^12
For year 5:
Cash outflow = 40,000(1+r)^11
For year 6:
Cash outflow = 40,000(1+r)^10
For year 7:
Cash outflow = 40,000(1+r)^9
For year 8:
Cash outflow = 40,000(1+r)^8
For year 9:
Cash outflow = 40,000(1+r)^7
For year 10:
Cash outflow = 40,000(1+r)^6
____________________________
Sum= 6,00,000

40,000[(1+r)^6 + (1+r)^7 + (1+r)^8 + (1+r)^9 + (1+r)^10 + (1+r)^11 + (1+r)^12 + (1+r)^13 + (1+r)^14 + (1+r)^15] = 6,00,000
So we see that sum of all (1+r)^n terms is 60/4 = 15
Using a financial calculation, we get 1+r = 1.04
Which means that r is approximately 4%.

Thus, if Mr. Greg invests at 4% per annum, he can get Rs. 6,00,000 by the end of 15 years.  
Hope this helped!