# 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,

1. What is the amount after 4 ​years? How much interest is​ earned?
2. What is the amount
3. What is the amount

6. 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 years

The monthly payment is ​\$_______

(A)

(B)

(C)

11. A family has a \$92,529​, 25​-year mortgage at 6% compounded monthly.

1. Find the monthly payment and the total interest paid.
2. 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.

1. 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?
2. 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.)