2.9.1: Exercises

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Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia
Rio Hondo College

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Section 2.9.1 Exercises

Suppose you invest $50 a month for 5 years into an account earning 8% compounded monthly. After 5 years, you leave the money in the account for another 25 years without making additional deposits. How much will you have in the end?
Kendra wants to be able to make withdrawals of $60,000 a year for 30 years after retiring in 35 years. How much will she have to save each year up until retirement if her account earns 7% interest?
You have $2,000 to invest, and want it to grow to $3,000 in two years. What interest rate would you need to find to make this possible if the money is compounded annually?

Exploration

Pay day loans are short term loans that you take out against future paychecks: The company advances you money against a future paycheck. Either visit a pay day loan company, or look one up online. Be forewarned that many companies do not make their fees obvious, so you might need to do some digging or look at several companies.
1. Explain the general method by which the loan works.
2. We will assume that we need to borrow $500 and that we will pay back the loan in 14 days. Determine the total amount that you would need to pay back and the effective loan rate. The effective loan rate is the percentage of the original loan amount that you pay back. It is not the same as the APR (annual rate) that is probably published.
3. If you cannot pay back the loan after 14 days, you will need to get an extension for another 14 days. Determine the fees for an extension, determine the total amount you will be paying for the now 28 day loan, and compute the effective loan rate.
Suppose that 10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.
1. How much money did you pay as your down payment?
2. How much money was your mortgage (loan) for?
3. What is your current monthly payment?
4. How much total interest will you pay over the life of the loan?
Referring to the same scenario from the problem above, suppose you check your loan balance on your mortgage. Only part of your payments have been going to pay down the loan; the rest has been going towards interest. You see that you still have $88,536 left to pay on your loan. Your house that you purchased for $110,000 is now valued at $150,000.
1. How much of the loan have you paid off? (i.e., How much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)
2. How much money have you paid to the loan company so far?
3. How much interest have you paid so far?
4. How much equity do you have in your home? (Equity is value minus remaining debt.)
Since interest rates have dropped, you consider refinancing the above mortgage at a lower rate of 6%.
1. If you took out a new 30 year mortgage at 6% for your remaining loan balance, what would your new monthly payments be?
2. How much interest will you pay over the life of the new loan?
Notice that if you refinance the loan above, you would be making payments on your home for another 30 years. In addition to the 10 years you've already been paying, that's 40 years total.
1. How much will you save each month because of the lower monthly payment?
2. How much total interest will you be paying? (You need to consider the amount from 3c and 4b.)
3. Does it make sense to refinance? (There isn't a correct answer to this question. Just give your opinion and your reasons.)
4. Would your answer change if you could refinance with a new loan term of 20 years, thus keeping the original 30-year time line?