Question

Terry will graduate in two years and has started planning for her future. Terry wants to buy a house five years after graduation and the down payment for a house is $70,000. As of right now, Terry has $8,000 in her account. Terry is certain that once she graduates, she can work in her family business and earn annual salary of $48,000, with a 3 percent raise every year. Terry plans to live with her parents for the first two years after graduation, which will enable her to minimise living expenses and save $15,000 each year. The next three years, Terry will have to live out on her own, as her younger sister will be graduating from college and has already announced her plan to move back into the family house. Thus, Terry will only be able to save 13 percent of her annual salary. Assume Terry is able to invest savings from her salary at 5 percent. What is the interest rate that Terry needs to invest the current savings account balance ($8,000) at in order to achieve her goal (the down payment for a house)?

Answer 1

Here time period = 2+5 = 7 years and Future value = 70,000

Cash flows are:

Year	Present savings	Salary (with 3% rise)	Savings (13% of salary for years 5 to 7)
0	8,000.00
1
2
3		48,000.00	15,000.00
4		49,440.00	15,000.00
5		50,923.20	6,620.02
6		52,450.90	6,818.62
7		54,024.42	7,023.17

Let the interest rate be x%.

Thus: 8000*(1+x)^7 + 15,000*1.05^4 + 15,000*1.05^3 +6620.02*1.05^2 + 6818.62*1.05 + 7023.17 = 70,000

or 8000*(1+x)^7 = 12,921.74

or 1+x = 1.070896

Thus interest rate = 7.09% (2 decimal place)

or 7.090 (3 decimal place)

or 7.0896 (4 decimal place)