Loans Practice. Math 107 Worksheet #23

Transcription

1 Math 107 Worksheet #23 Loans Practice M P r ( 1 + r) n ( 1 + r) n =, M = the monthly payment; P = the original loan amount; r = the monthly interest rate; n = number of payments 1 For each of the following, find a) the monthly payment; b) the total amount paid over the term of the loan; c) the total amount of interest paid on the loan. Ex. 1 A home mortgage of $150,000 at 6% interest for 15 years. Ex. 2 A home mortgage of $150,000 at 6% interest for 30 years. 1. A second mortgage of $50,000 at 7% interest for 10 years. 2. A second mortgage of $50,000 at 7% interest for 15 years. 3. A car loan of $10,000 at 5% interest for 5 years. 4. A car loan of $10,000 at 5% interest for 4 years.

2 ln M n = ln 1 ( M ) P r ( + r) will give us the number of payments we need to make in order to pay off a loan early. For each of the following, find a) how long it will take to pay off the loan if you pay $100 extra a month (use your answer from the previous page to calculate your monthly payment); b) the total amount paid over the term of the loan; c) the total amount of interest paid on the loan; d) the amount of money you saved. Ex. 1 A home mortgage of $150,000 at 6% interest. Ex. 2 A home mortgage of $150,000 at 6% interest. 1. A second mortgage of $50,000 at 7% interest. 2. A second mortgage of $50,000 at 7% interest. 3. A car loan of $10,000 at 5% interest. 4. A car loan of $10,000 at 5% interest.

3 Credit Card Practice Worksheet #24 Use a separate sheet for all of your answers. 1. Let s assume you have a credit card with an outstanding balance of $2,000 (P). Start with this amount. 2. Calculate your annual interest rate given that your interest rate is 4% + prime (you will need to find the current prime interest rate on the web). 3. Calculate your monthly interest rate (as a decimal, r). 4. Use your monthly interest rate (as a decimal) to calculate the interest you will pay on your outstanding balance in one month. 5. Add the interest to your outstanding balance to find your new balance. 6. Calculate your minimum payment (M). Your minimum payment is 2% of your new balance. 7. Now, we will compute how many payments you will need to make in order to pay off your original ln( M ) M P r balance on your credit card. Use the formula n = (the one we used in class). Round the ln( 1 + r) answer to the nearest whole number. This is the number of payments you need to make. 8. Calculate how much money you will pay if you make the minimum payment for that number of payments. This is the total amount of money you will pay back to the credit card company. 9. Calculate how much total interest you will pay for your purchases if you pay that total amount of money, but you only spent your original balance on your apartment initially. 10. Compare your total interest to your original balance. Write a sentence stating what you discovered. 11. How long will it take you to pay off your credit card (in years)? 12. A. In reality, would you have your credit card paid off by the time you found in #11? B. What is the most likely reason your credit card would not be paid off on time? 13. Will you change how you use credit now that you have seen the true cost?

4 Interest Practice Worksheet #25 Simple Interest: I = P r t, I = interest; P = the original loan amount; r = the annual interest rate; t = number of Compound Interest: years n ( 1 + r), A = amount in the bank; P = the original loan amount; r = the period interest rate; = number of periods A = P n For each of the following, find a) the interest earned; b) the total amount in the account. Ex. 1 Simple interest on $1200 at 4% for 5 years. Ex. 2 Compound interest on $1200 at 4% for 5 years. a) compounded annually b) compounded quarterly c) compounded monthly Ex. 3 Compound interest on $1200 at 4% for 5 years using the future value table. d) compounded annually e) compounded quarterly f) compounded monthly

5 Annuities: For each of the following, find a) the interest earned; b) the total amount in the account. Ex. 4 Compound interest on $1200/yr. at 4% for 10 years using the future value of an annuity table. Ex. 5 Compound interest on $100/mo. at 4% for 10 years using the future value of an annuity table. Ex. 6 Compound interest on $2400/yr. at 4% for 5 years using the future value of an annuity table. Ex. 7 Compound interest on $200/mo. at 4% for 5 years using the future value of an annuity table. Ex. 8 Find the present value of $1,000,000 in 10 years. Ex. 9 Find the present value of $1,000,000 in 20 years.

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