1. Make the first three rows of an amortization table for the following loan. You buy a house for $145,000 by paying 20% down and then making monthly payments for the next 30 years. The interest rate is 7.5% compounded monthly.

The down payment is $29000. So the remaining amount to be financed is $116,000.

Now this is the present value of an annuity.

116000=R[1-(1.00625)^-360]/.00625

116000 = 143.0176273 R

R = $811.09

Payment #	Payment	Interest Paid	Principal Paid	Outstanding Balance
0				116000
1	$811.09	$725.00	$86.09	$115,913.91
2	$811.09	$724.46	$86.63	$115,827.28
3	$811.09	$723.92	$87.17	$115,740.11
4	$811.09	$723.38	$87.71	$115,652.40
5	$811.09	$722.83	$88.26	$115,564.14
6	$811.09	$722.28	$88.81	$115,475.33

2. A company want s fund an endowment which pays IHCC $50,000 per year at the end of each year. How much money do they need to give the school if the interest rate is 8% compounded quarterly? Hint: this is a perpetuity. Find the effective interest rate.

Effective rate = (1 + i)^n – 1

= 1.02^4 – 1

= 8.24%

50000 = P.08243216

P = $606559.38

3. Given an investment of $7000 compounded at 9% quarterly, what will its value be after 26 years?

This is a compound interest problem as there is only one payment.

A(26)=7000(1+.09/4)^104

A(26) = $70808.11

4. What is the effective interest rate of 18% compounded monthly?

5. If you put $50 at the end of each month into an annuity which earns 15% per year compounded monthly, how much will you have in 25 years? Ans: $162,176.48

This is the future value of an ordinary annuity:

6. You buy a Jeep Grand Cherokee for $28,000 and put 10% down. The financing is secured at 8% compounded monthly. What are the monthly payments if you finance the Jeep for 36 months? 48 months? 60 months? What is the total amount paid on each of the above loans?

36months: $789.68

Total Paid is 789.68*36= $28428.48

48 months:

$615.21

Total Paid: 48(615.21)=$29530.08

60 months: $510.97

Total Paid: 60(510.97) = $30658.20

7. Fred needs to pay back Vinnie the loan shark $50,000 for a gambling debt. If an interest rate of 21% per year is charged on the unpaid balance, create an amortization chart so that Fred pays the loan back in 5 years with payments at the end of each year.

Payment #	Payment	Interest Paid	Principal Paid	Outstanding Balance
0				50000
1	$17,088.27	$10,500.00	$6,588.27	$43,411.73
2	$17,088.27	$9,116.46	$7,971.81	$35,439.92
3	$17,088.27	$7,442.38	$9,645.89	$25,794.03
4	$17,088.27	$5,416.75	$11,671.52	$14,122.51
5	$17,088.24	$2,965.73	$14,122.51	$0.00

8. Thomas wants to have $1,000,000 when he retires in 35 years. How much does he need to deposit at the beginning of each month in a retirement account which earns 8.5% per year compounded monthly? What is the value of that amount in today’s money if there was an annual inflation rate of 4 %?

This is a future value of an annuity due.

9. This year it is projected that in the United States there will approximately 156 billion gallons of gas used by automobiles. This amount is expected to increase by 2.5 billion gallons per year over the next 15 years. How many gallons will be used 15 years from now. How many total gallons will be used this year and over the next 15?

This is an arithmetic sequence:

156 + 158.5 +161 + …

d = 2.5

our explicit function will be:

So the amount in 15 years will be:

P = 156 + 2.5(15)

P = 193.5 billion gallons of gas

The sum will be:

or 2.796 trillion gallons of gas.