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In: Finance

Chee will graduate in two years and has started planning for his future. Chee wants to...

Chee will graduate in two years and has started planning for his future. Chee wants to buy a house six years after graduation and the down payment for a house is $120,000. As of right now, Chee has $15,000 in his savings account. Chee is fairly certain that once he graduates, he can work in his family business and earn annual salary of $48,000, with a 3 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 four 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 13 percent of his annual salary. Assume that Chee is able to invest savings from his salary at 5 percent. What is the interest rate Chee needs to invest the current savings account balance ($15,000) at in order to achieve his goal (the down payment for a house)?

Solutions

Expert Solution

Amount set aside for downpayment in year 1 and year 2 = 25000

Amount earned in year 3 = 48000 *1.03^2 =50923.2

Amount set aside for year 3 = 50923.2 * 0.13 = 6620.016

Future value = present value * ( 1 + int rate )^ no of years

Pariculars Year Total
1 2 3 4 5 6
Amount Earned 48000 49440 50923.2 52450.896 54024.42288 55645.15557
Amount sent aside 25000 25000 6620.016 6818.61648 7023.174974 7233.870224
Future Value 31907 30388 7663.496 7517.52467 7374.333723 7233.870224 92083.92

We have 92083.92 out of 120000 down payment hence amount left = 120000 - 92083.92 = 27916.08

There is 8 years from current to the date of sown payment

So the return on savings will be as below

27916.08 = 15000 * ( 1+ r)^8

r = (27916.08 /15000) ^ 1/ 8 - 1 = 8.07%

the interest rate Chee needs to invest the current savings account balance ($15,000) at in order to achieve his goal (the down payment for a house = 8.07%


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