3. Suppose a particular person decides to start saving money to buy a house. Suppose they start with an initial balance of y0 dollars and they invest their money and earn 12% interest per year. Suppose they supplement their investment with x[n] dollars invested each month immedately following the initial investment (e) Now, assuming the initial investment is y0 = 10,000 dollars with x[n] = 0 (zero additional dollars invested), find the balance across time. To answer this problem, assume your answer is of the form y[n] = c(1.01)"u[n] and find c. (f) How many years are required to obtain a $100,000 balance based on the invest- ment strategy in part (e)? (g) Find the account balance across time assuming zero initial investment, but that $500 is invested each month, i.e., y0] = 0,x(n = 500. To answer this problem, you can convolve the impulse response from part (c) with x[n] = 500u[n]. (h) How many years are required to obtain a $100,000 balance based on the invest- ment strategy in part (g)? (i) Finally, assuming the initial investment is y0 = 10,000 dollars and an addi- tional investment of $500 each month, find the account balance across time. To answer this problem, you can simply add your results from parts (e) and (g). 3. Suppose a particular person decides to start saving money to buy a house. Suppose they start with an initial balance of y0 dollars and they invest their money and earn 12% interest per year. Suppose they supplement their investment with x[n] dollars invested each month immedately following the initial investment (e) Now, assuming the initial investment is y0 = 10,000 dollars with x[n] = 0 (zero additional dollars invested), find the balance across time. To answer this problem, assume your answer is of the form y[n] = c(1.01)"u[n] and find c. (f) How many years are required to obtain a $100,000 balance based on the invest- ment strategy in part (e)? (g) Find the account balance across time assuming zero initial investment, but that $500 is invested each month, i.e., y0] = 0,x(n = 500. To answer this problem, you can convolve the impulse response from part (c) with x[n] = 500u[n]. (h) How many years are required to obtain a $100,000 balance based on the invest- ment strategy in part (g)? (i) Finally, assuming the initial investment is y0 = 10,000 dollars and an addi- tional investment of $500 each month, find the account balance across time. To answer this problem, you can simply add your results from parts (e) and (g)
