# compounding interest and value of money

Please see the attached file.

1. Find the simple interest for $4902 at 9.5% for 11 months.

2. Find the compound amount for $312.45 at 6% compounded semiannually for 16 years.

3. Find the amount of interest earned by depositing $12,903.45 at 10.37% compounded quarterly for 29 quarters.

4. Find the present value of $17,650 in 4 years, 8% compounded quarterly.

5. Write the first four terms of the geometric sequence with a = 4 and r = ½.

6. Find the fifth term of the geometric sequence with a = -2 and r = -2.

7. Find the sum of the first five terms of the geometric sequence with a = 8000 and r = -1/2.

9. Find the future value of the following annuity. $500 deposited at the end of each 6-month period for 8 years; money earns 6% compounded semiannually.

10. Find the amount of each payment that must be made into a sinking fund to accumulate the following amount. (Recall, in a sinking fund, payments are made at the end of every interest period.)

$57,000; money earns 6% compounded semiannually for 8 ½ years.

11. Find the present value of the following ordinary annuity. Payments of $877.34 monthly for 17 months at 9.4% compounded monthly.

12. Find the monthly house payment for the following mortgage. $56,890 at 10.74% for 25 years.

13. Personal Finance: Michael Garbin owes $5800 to his mother. He has agreed to reapy the money in 10 months at an interest rate of 10.3%. How much will he owe in 10 months? How much interest will he pay?

14. Personal Finance: To buy a new computer, Mark Nguyen borrows $3250 from a friend at 9% interest compounded annually for 4 years. Find the compound amount he must pay back at the end of the 4 years.

15. When the Lee family bought their home, they borrowed $115, 700 at 10.5% compounded monthly for 25 years. If they make all 300 payments, repaying the loan on schedule, how much interest will they pay? (Assume the last payment is the same as the previous ones.)

16. Find the monthly house payments for each mortgage. $51,607; 13.6% compounded monthly; 32 monthly payments

17. $3200; 8% compounded quarterly; 10 quarterly payments, Find payments.

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#### Solution Summary

The solution explains and provides formulas for calculations of the value of money, such as present value, future value of ordinary annuity, monthly payment of mortgage, and payment to sinking fund, etc.

Simple and compound interest; present value concept; and TVM.

1. Explain what is the difference between "simple" and "compound" interest? Provide some of the uses of compound interest in business. What are the effects of using compound interest when evaluating future value transactions and calculations.

2. What is "present value"? What is an example of the "present value" concept? How does a single cash flow present value example differ from an annuity calculation?

3. How is a home mortgage an example of TVM? How can you show that more interest is paid at the beginning of a loan period than at the end?

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