1. Mrs. Hart, at age 65, can expect to live for 25 years. If she can invest at 8% per annum compounded monthly, how much does she need now to guarantee herself $300 every month for the next 25 years?
2.Jeremy takes out a 30-year mortgage of 220000 dollars at an annual interest rate of 7 percent compounded monthly, with the first payment due in one month. How much does he owe on the loan immediately after the 87th payment?
3.Ralph wants to quit his job and move to Hawaii on December 25, 2015. Once there, he anticipates that he will need to make annual withdrawals of 12500 dollars (starting on December 25, 2016) to supplement his income from working as a cabana boy, and he wants the money to last 10 years (i.e. he'll make 10 withdrawals total). His plan is to make annual deposits, starting on December 25, 2000 and ending on December 25, 2015, into an account paying 7.6 percent interest rate compounded annually. How large should each deposit be for Ralph to realize his goal?
4.Dave takes out a 23-year mortgage of 300000 dollars for his new house. Dave gets an interest rate of 14.4 percent compounded monthly. He agrees to make equal monthly payments, the first coming in one month. After making the 67th payment, Dave wants to buy a boat, so he wants to refinance his house to reduce his monthly payment by 700 dollars, and to get a better interest rate. In particular, he negotiates a new rate of 8.4 percent compounded monthly, and agrees to make equal monthly payments (each 700 dollars less than his original payments) for as long as necessary, followed by a single smaller payment. How large will Dave's final loan payment be?
2.Jeremy takes out a 30-year mortgage of 220000 dollars at an annual interest rate of 7 percent compounded monthly, with the first payment due in one month. How much does he owe on the loan immediately after the 87th payment?
3.Ralph wants to quit his job and move to Hawaii on December 25, 2015. Once there, he anticipates that he will need to make annual withdrawals of 12500 dollars (starting on December 25, 2016) to supplement his income from working as a cabana boy, and he wants the money to last 10 years (i.e. he'll make 10 withdrawals total). His plan is to make annual deposits, starting on December 25, 2000 and ending on December 25, 2015, into an account paying 7.6 percent interest rate compounded annually. How large should each deposit be for Ralph to realize his goal?
4.Dave takes out a 23-year mortgage of 300000 dollars for his new house. Dave gets an interest rate of 14.4 percent compounded monthly. He agrees to make equal monthly payments, the first coming in one month. After making the 67th payment, Dave wants to buy a boat, so he wants to refinance his house to reduce his monthly payment by 700 dollars, and to get a better interest rate. In particular, he negotiates a new rate of 8.4 percent compounded monthly, and agrees to make equal monthly payments (each 700 dollars less than his original payments) for as long as necessary, followed by a single smaller payment. How large will Dave's final loan payment be?