# Compound and Simple Interest, PV Annuities, and FV Sinking Funds

Congratulations! You have been hired by XYZ Advertising. You have been placed on an advertising team with your first big client, a local financial institution; however, you are somewhat nervous to join the advertising team as your financial knowledge and background are somewhat limited. Thus, before putting together an ad campaign with your fellow team members, you need to brush up on the particular terms and calculations that you are unfamiliar with that are listed in the advertising layout guide.

There are many terms used in the world of financial mathematics. It is important that these terms and their calculations are understood before working with the financial institution and the advertising team.

For this Discussion Board, use the library, Internet, and other resources to discuss the following financial terms, and give an actual calculated example of each:

Compound Interest and Simple Interest

1) Present Value, Annuities, and Amortization

2) Future Value and Sinking Funds

3) Give examples of specific organizations or individuals that may wish to utilize these concepts. Explain how and why they may want to use these concepts.

Objective: Illustrate compound interest formulas, using them to find future values and present values of a dollar; explain annuities and find the future value or present value of an annuity; illustrate amortization of certain types of installment loans and sinking funds.

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#### Solution Preview

Definition:

Present value is the value in today's dollars of a future payment discounted back to present at the required rate of return.

Future value is the amount of money that will grow to at some point of the future.

Simple interest is interest that is calculated on the principal for the entire period that it is borrowed.

Compound interest is interest that is calculated on both the principal and the accrued interest.

Annuities are series of equal cash flows, spaced evenly over time.

Amortization is the reduction of the value of an asset by prorating its cost over a period of years.

Sinking funds is an account in which you will set aside money on regular basis to accrue interest in order to pay off a debt in full after a specific amount of time.

Discussion:

An individual should always pay attention to these concepts when it comes to borrow or save money. Money loses value over time because of inflation. Thus, assuming that the inflation rate stays the same over a period, he can ...

#### Solution Summary

Compounds and simple interest, PV, annuities, FV, and sinking funds are discussed.

Interest, value of annuity, mortgage payment

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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