III I u Lidl ulje! Use this to explain your results. 5. Compound interest. Suppose ao dollars are deposited in a bank that pays 5% interest per year, compounded quarterly. After one quarter the value of the account is ao x (1 + (0.05)/4) dollars. At the end of the second quarter, the bank pays interest not only on the original amount ao, but also on the interest earned in the first quarter; 130 thus the value of the investment at the end of the second quarter is 10 x (1 + (0.05)/4)3 dollars, sao x (1 + (0.05)/4)] (1 + (0.05)/4) = 10 x (1 + (0.05)/4)2 the third quarter the bank pays interest on this dollars. At the end of the third quarter the bank pays amount, so that the account is now worth ao x (1 + (0.05)/4)3 and at the end of the whole year the investment is finally worth ao x (1 + (0.05)/4) dollars. In general, if a, dollars are deposited at an annual interest rat compounded n times per year, then the account value after one year is xin ao x Zy(x) where Ly(x) = (1 + # ). This is the compound interest formula. It is well known that for fixed x, limn-o In(x) = exp(x). well conditioned or ill conditioned? (b) Use MATLAB to compute In (x) for x = 0.05 and for n = 1, 10, 102, ..., 1015. Use format long e so that you can see if your results are converging to exp(x), as one might expect. Turn in a tabi with your results and a listing of the MATLAB command(s) you usca to compute these results. (c) Try to explain the results of mort (n) III I u Lidl ulje! Use this to explain your results. 5. Compound interest. Suppose ao dollars are deposited in a bank that pays 5% interest per year, compounded quarterly. After one quarter the value of the account is ao x (1 + (0.05)/4) dollars. At the end of the second quarter, the bank pays interest not only on the original amount ao, but also on the interest earned in the first quarter; 130 thus the value of the investment at the end of the second quarter is 10 x (1 + (0.05)/4)3 dollars, sao x (1 + (0.05)/4)] (1 + (0.05)/4) = 10 x (1 + (0.05)/4)2 the third quarter the bank pays interest on this dollars. At the end of the third quarter the bank pays amount, so that the account is now worth ao x (1 + (0.05)/4)3 and at the end of the whole year the investment is finally worth ao x (1 + (0.05)/4) dollars. In general, if a, dollars are deposited at an annual interest rat compounded n times per year, then the account value after one year is xin ao x Zy(x) where Ly(x) = (1 + # ). This is the compound interest formula. It is well known that for fixed x, limn-o In(x) = exp(x). well conditioned or ill conditioned? (b) Use MATLAB to compute In (x) for x = 0.05 and for n = 1, 10, 102, ..., 1015. Use format long e so that you can see if your results are converging to exp(x), as one might expect. Turn in a tabi with your results and a listing of the MATLAB command(s) you usca to compute these results. (c) Try to explain the results of mort (n)
