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# Finite Mathematics

1. The unpaid balance at the start of a 28-day billing cycle was $997.81. A $6,000 purchase was made on the first day of the billing cycle and a $100 payment was credited to the account on day 21. How much interest will be charged at the end of the billing cycle? Assume that the annual interest rate on a credit card is 26.16 % and interest is calculated by the average daily balance method.At the end of the billing cycle, $________ will be charged in interest.(Round to the nearest cent as needed.)2. The unpaid balance at the start of a 30-day billing cycle was $615.37. No purchases were made during the billing cycle and a payment of $615.37 was credited to the account on day20. Find the unpaid balance at the end of the billing cycle. Assume that the annual interest rate on a credit card is 20.36 % and interest is calculated by the average daily balance method.The unpaid balance at the end of the billing cycle is $_______(Round to the nearest cent as needed.)3. The unpaid balance at the start of a 30-day billing cycle was $791.99. A purchase of $59.81 was made on day 15. No payment was made during the billing cycle and a late fee of $31 was charged to the account on day 23. Find the unpaid balance at the end of the billing cycle. Assume that the annual interest rate on a credit card is 20.39 % and interest is calculated by the average daily balance method.The unpaid balance at the end of the billing cycle is $_______(Round to the nearest cent as needed.)4. A payday loan is a short-term loan that is repaid on the next payday, often by giving the lender electronic access to a personal checking account. Some states have statutes that regulate the fees that may be charged for payday loans. Suppose that, in a certain state, finance charges on a payday loan may not exceed 17.7 % of the amount advanced. Find the annual interest rate if $300 is borrowed for 11 days at the maximum allowable charge.The annual interest rate is______ %.(Round to the nearest percent as needed.)5. If $700 is invested at 8 % compounded(A) annually, (B) quarterly, (C) monthly,What is the amount after 4 years? How much interest is earned?What is the amountWhat is the amount6. How long will it take money to triple if it is invested at 5 % compounded monthly? 6.4% compounded continuously?It will take about ____years at 5 % compounded monthly.(Round to two decimal places as needed.)It will take about ____years at 6.4% compounded continuously.(Round to two decimal places as needed.)7. Use graphical approximation techniques or an equation solver to approximate the desired interest rate. A person makes annual payments of $1000 into an ordinary annuity. At the end of 5 years, the amount in the annuity is $5720.98. What annual nominal compounding rate has this annuity earned?Type the interest rate:______ %(Round to 2 decimal places.)8. Use graphical approximation techniques or an equation solver to approximate the desired interest rate. An employee opens a credit union account and deposits $110 at the end of each month. After one year, the account contains $1325.09. What annual nominal rate compounded monthly has the account earned?The annual nominal rate is ______%.(Round the final answer to two decimal places as needed. Round all intermediate values to six decimal places as needed.)9. A woman borrows $4000 at 12 % compounded monthly, which is to be amortized over 3 years in equal monthly payments. For tax purposes, she needs to know the amount of interest paid during each year of the loan. Find the interest paid during the first year, the second year, and the third year of the loan. [Hint: Find the unpaid balance after 12 payments and after 24 payments.]The interest paid during the first year is $________(Round to the nearest cent as needed.)10. A family has a $111,408 , 30 -year mortgage at 6.3% compounded monthly. Find the monthly payment. Also find the unpaid balance after the following periods of time.(A) 10 years (B) 20 years (C) 25 yearsThe monthly payment is $_______(A)(B)(C)11. A family has a $92,529 , 25 -year mortgage at 6% compounded monthly.Find the monthly payment and the total interest paid.Suppose the family decides to add an extra $100 to its mortgage payment each month starting with the very first payment. How long will it take the family to pay off the mortgage? How much interest will the family save?12. An ordinary annuity pays 8.04 % compounded monthly.A person deposits $100 monthly for 30 years and then makes equal monthly withdrawals for the next 15 years, reducing the balance to zero. What are the monthly withdrawals? How much interest is earned during the entire 45-year process?If the person wants to make withdrawals of 1,500 per month for the last 15 years, how much must be deposited monthly for the first 30 years?13. A couple wishes to borrow money using the equity in their home for collateral. A loan company will loan them up to 70% of their equity. They purchased their home 10 years ago for $60,670. The home was financed by paying 15 % down and signing a 15 -year mortgage at 9 % on the unpaid balance. Equal monthly payments were made to amortize the loan over the 15 -year period. The net market value of the house is now $100,000. After making their 120th payment, they applied to the loan company for the maximum loan. How much (to the nearest dollar) will they receive?Amount of loan: $_______(Round to the nearest dollar.)14. A person purchased a $236,124 home 10 years ago by paying 15 % down and signing a 30-year mortgage at 9.9 % compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 20 -year mortgage at 5.4% compounded monthly. How much interest will refinancing save?Money Saved: $______(Round to the nearest cent as needed.)15. A discount electronics store offers to let you pay for a $1000 stereo in 12 equal $87 installments. The store claims that since you repay $1044 in 1 year, the $87 finance charge represents a 4.4 % annual rate. This would be true if you repaid the loan in a single payment at the end of the year. But since you start repayment after 1 month, this is an amortized loan, and 4.4 % is not the correct rate. What is the annual nominal compounding rate for this loan? Use graphical approximation techniques or an equation solver to approximate the interest rate. Express the answer as a percentage.The actual annual nominal compounding rate for this loan is_______ %.(Type an integer or decimal rounded to two decimal places as needed.)