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Quinn takes out a loan of $350,000 to purchase a small condo in Boston. The bank agrees to lend to him at an 8% annual interest rate, compounded monthly.
To repay the loan, Quinn makes monthly payments of $P over 15 years.
Determine the value of P to the nearest dollar.
Calculate the total payments Quinn makes to the bank.
Hence find the total interest paid by Quinn.
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Jacob is choosing between two ways to save up for a vacation planned 7 years from now. He is considering two different strategies to save a total of €Q for his vacation.
Option A: Deposit €4000 today in an account that earns 4.2% annual interest, compounded monthly.
Option B: Deposit €P at the end of each month until the vacation in an account that earns 5% annual interest, compounded monthly.
Calculate, to the nearest euro, the value of €Q.
Find the value of P, giving your answer to two decimal places.
Determine which option yields greater total interest, and state by how much.
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An arithmetic sequence has 2u6=S6=5, where S6 is the sum of the first 6 terms. Find the second term, u2, of the sequence.
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An arithmetic sequence has u3=5 and u7=−7.
Find the common difference d and the first term u1 of the sequence.
Hence find u10.
Find S10.
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A geometric sequence has u3=3 and u6=98. Find S∞ for this sequence.
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Ella invests $500 in a savings account that earns 4% interest per annum, compounded quarterly.
Find an expression for the balance of Ella's savings after n years.
Calculate the value of Ella's savings after 12 years. Give your answer to the nearest dollar.
Ella wants to purchase a racing bike for $700.
Find the number of years after which her savings will be sufficient to purchase the bike.
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