Question

You are a very forward-looking college student with 2 years to go before graduation. You would like to be able to purchase your first home 4 years after graduation (6 years from now) and will need $50,000 for the down payment. You have been a good saver and currently have $15,000 in your savings account (this is from before college and you will not be able to save any more until after graduation). Assume that your salary the first year after graduation will be $40,000 and will grow 4% each year after that. Your plan is to live with your college roommates for the first 2 years after graduation and then rent on your own. For the 2 years after college you are living with your roommates you expect to be able to save $10,000 per year, but for the 2 years after that you will only be able to save 10% of your gross income. All of the savings from your income will go into a separate account than your current savings and earn 8% annually (compounded annually). What interest rate must you earn on your current savings in order to have the $50,000 you will need for the down payment on your house 6 years from now? Hint: Draw a timeline that shows all the cash flows for years 0 through 6. Remember, you want to buy a house 6 years from now and your contribution from your first year’s salary will be at the end of period 3.

Answer 1

Drawing Timelines to show cashflows available per year till 6th Year. Yr. O Yr.1 | Yr. 2 Yr. 3 Yr. 4 Yr. 5 Yr. 6 Bal. 15 K Sal. 40K Sal. 41.6K Sal. 43.26 Sal. 44.99 K Page 1

Calculating Future values of Cashflows at different Interest Rates Year Particulars Balance Interest FVF @ 8% FVCF Period 0 Op. Balance 15,000.00 6 Years 1.59 23,803.11 3 Salary Saved 10,000.00 3 Years 1.26 12,597.12 4 Salary Saved 10,000.00 2 Years 1.17 11,664.00 5 Salary Saved 4,326.00 1 Years 1.08 4,672.08 6 Salary Saved 4,499.00 0 Years 1.00 4,499.00 43,825.00 | 57235.31484 FVF @ 6% FVCF FVF @ 4% FVCF FVF @ 3% FVCF 1.42 21,277.79 1.27 18,979.79 1.19 17,910.78 1.19 11,910.16 1.12 11,248.64 1.09 10,927.27 11,236.00 10,816.00 1.06 10,609.00 1.06 4.585.56 1.04 4,499.04 1.03 4,455.78 1.00 4,499.00 1.00 4,499.00 1.00 4,499.00 53508.50668 50042.46528 48401.83445 1.08 Therefore, It can be seen that, if Interest is paid at 4%, saving amount approximates 50000. Therefore, interest rate shall be at least 4% to have savings of 50000. Page 2