### What will be the size of his first payment

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Question :1) Ralph has just borrowed 1480 dollars to purchase a new stereo, at a nominal rate of interest of 11.4 percent convertible monthly. Although he is charged interest from the moment he borrows the money, the first payment is not due for 10 months. If he will make 24 monthly payments, how much interest is in the 17th payment?

2) Suppose that a loan is being repaid with 20 annual payments, with the first payment coming one year from now. The first 5 payments are for 240 dollars, the next 8 are 300 dollars each, and the final 7 are 430 dollars each. If the effective rate of interest is 7.1 percent, how much interest is in the 11th payment?

3) Craig borrows 6500 dollars a year to pay for college expenses, starting on September 1, 2000 - the day he starts college - and ending on September 1, 2004. (i.e. that''s 5 withdrawals total). After graduation, he decides to go to graduate school in mathematics, and his loans are deferred (i.e. they still accrue interest, but no payments are due). After graduation from graduate school, he needs to begin paying off his loans. He will make monthly payments for 6 years, and each payment will increase by 1.5 percent. His payments will begin on July 1, 2007, exactly 6 years and 10 months after he started college. If he pays a nominal rate of 6.6 percent convertible monthly for the entire life of the loans, what will be the size of his first payment?

4) Alex Rodriguez recently signed a contract with the Texas Rangers that will pay him approximately 250 million dollars over the next 10 years. In this problem, assume that he will receive his pay annually in 25 million dollar installments, and that he has just received the first payment. Suppose that he decides to set aside a fixed amount each year to fund a perpetuity of 19500000 dollars per year for his retirement, with the first payment to come in 17 years. If the effective rate of interest is 8.5 percent, how much of his annual salary will be left, after he makes his perpetuity investment?

5) An annuity makes a sequence of annual payments (starting a year from now) of 2600 dollars. If the payments were to last twice as long, the present value of the annuity would increase by 35 percent. If the payments were to last 3 times as long, what would be the present value now of the final payment?

6) Nicole borrows 300000 dollars for 10 years at a nominal rate of 4.5 percent convertible monthly. She has the option of paying off the loan using either the amortization or sinking fund method. If the sinking fund has an interest rate of 5.7 percent convertible monthly, how much will she save each month by going with the better method? (Assume monthly payments and deposits.) (Note: you''ll need to decide which method is the better one.)

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