Exam Review Suggestions

•	Find simple interest.
•	Find compound amount.
•	Find effective annual rate so that two savings accounts can be compared.
•	Find future value of an ordinary annuity.
•	Find the payment amount necessary to create a certain sinking fund.
•	Find mortgage payment.
•	Find amount of principal remaining on a mortgage after paying for several years.
•	Find total amount of interest paid over the life of a contract.
•	Find the amount of a mortgage if given the payment, frequency of payment, interest rate and length of mortgage.
•	Find the price house which could be afforded if a certain amount is available for payment and either a certain amount is available for a down payment or enough is available for a specified percentage for a down payment.
•	Find the amount of payment into an ordinary annuity in order to be able to draw out a certain amount for retirement for a given number of years. This is a two-stage problem. 

The finance formulas will be provided.

Finance Formulae

Simple interest 

Compound interest 

Continuous compounding 

Effective annual rate 
Future value (ordinary annuity) 
Sinking fund deposit 
Present value (ordinary annuity) 
Mortgage payment 

Sample Problems
1.  The Jones family is trying to save money towards college tuition for their 3-year old child.  They pay $59.99 per month for digital cable.  If, instead of subscribing to cable, they deposit $59.99 per month into a savings account that pays 3.2% interest, how much money will they have accumulated after 15 years?  

2. The Smith family needs $150,000 to buy a house.  They take out a 30-year mortgage with an interest rate of 7.8 % compounded monthly.

a. What is their monthly payment?

b. After exactly 20 years of making payments, what is their payoff amount?  (In other words, what is their remaining principal at this time?)

3. For ten years Sally makes $200 monthly payments to a fund earning 6% annual rate of interest compounded monthly. At the end of ten years she stops making payments, but leaves the accumulated amount in the fund for twenty years earning interest at same rate as before. How much will she have at the end of this twenty year period? 

4. When the Garcias had their first child, they decided to save $80,000 for her college education. They decided to make monthly payments into a trust fund that earns 6.2% annual interest compounded monthly. If they are to have the $80,000 by her 18th birthday, how large should the monthly payments be?

5. Two investments are considered to plan for a retirement in 10 years: 

Option 1: putting $5000 into an account that pays 4% compounded continuously or 
Option 2: making quarterly payments of $150 into an account that pays 4% compounded quarterly?

a. Which will result in a larger balance after 10 years?

b. Find the interest earned for each case in part a.

6. One bank offers an interest rate of 3.25% with interest compounded annually. Another bank offers a rate of 3.22% with interest compounded monthly. Which is the better deal?  

7. Suppose that you buy a $110,000 house with a down payment of $10,000 and a 20 year mortgage at a rate of 6.35% compounded monthly. 

a. What will your monthly mortgage payment be?

b. How much will you end up paying for the house?

c. After 15 years, how much is owed on the house?