Question

Chee will graduate in two years and has started planning for his future. Chee wants to buy a house five years after graduation and the down payment for a house is $100,000. As of right now, Chee has $8,000 in his savings account. Chee is fairly certain that once he graduates, he can work in his family business and earn annual salary of $55,000, with a 5 percent raise every year. Chee plans to live with his parents for the first two years after graduation, which will enable him to minimise living expenses and put away $25,000 each year. The next three years, Chee will have to live out on his own, as his younger sister will be graduating from college and has already announced her plan to move back into the family house. Thus, Chee will only be able to save 12 percent of his annual salary. Assume that Chee is able to invest savings from his salary at 6 percent. What is the interest rate Chee needs to invest the current savings account balance ($8,000) at in order to achieve his goal (the down payment for a house)?

Answer 1

Here Chee needs $100,000 (future value) in (2+5) = 7 years time.

The various cash flows are:

Year	Present savings	Salary (with 5% rise)	Savings (12% of salary for years 5 to 7)
0	8,000.00
1
2
3		55,000.00	25,000.00
4		57,750.00	25,000.00
5		60,637.50	7,276.50
6		63,669.38	7,640.33
7		66,852.84	8,022.34

Let the interest rate be x%.

Thus 8,000*(1+x)^7 +  25,000*(1.06^4) + 25,000*(1.06^3) + 7276.50*(1.06^2) + 7640.33*1.06 + 8022.34 = 100,000

or 8000*(1+x)^7 = 14,365.71

or (1+x)^7 = 1.79571

or 1+x = 1.087225

Thus rate of interest = 8.72% (2 decimal place)

or 8.723% (3 decimal place)

or 8.7225% (4 decimal place)