A friend lends you [latex]$200[/latex] for a week, which you agree to repay with [latex]5\%[/latex] one-time interest. How much will you have to repay?
Suppose you obtain a [latex]$3,000[/latex] T-note with a [latex]3\%[/latex] annual rate, paid quarterly, with maturity in [latex]5[/latex] years. How much interest will you earn?
A T-bill is a type of bond that is sold at a discount over the face value. For example, suppose you buy a [latex]13[/latex]-week T-bill with a face value of [latex]$10,000[/latex] for [latex]$9,800[/latex]. This means that in [latex]13[/latex] weeks, the government will give you the face value, earning you [latex]$200[/latex]. What annual interest rate have you earned?
Suppose you are looking to buy a [latex]$5000[/latex] face value [latex]26[/latex]-week T-bill. If you want to earn at least [latex]1\%[/latex] annual interest, what is the most you should pay for the T-bill?
You deposit [latex]$300[/latex] in an account earning [latex]5\%[/latex] interest compounded annually. How much will you have in the account in [latex]10[/latex] years?
How much will [latex]$1000[/latex] deposited in an account earning [latex]7\%[/latex] interest compounded annually be worth in [latex]20[/latex] years?
You deposit [latex]$2000[/latex] in an account earning [latex]3\%[/latex] interest compounded monthly.
How much will you have in the account in [latex]20[/latex] years?
How much interest will you earn?
You deposit [latex]$10,000[/latex] in an account earning [latex]4\%[/latex] interest compounded monthly.
How much will you have in the account in [latex]25[/latex] years?
How much interest will you earn?
How much would you need to deposit in an account now in order to have [latex]$6,000[/latex] in the account in [latex]8[/latex] years? Assume the account earns [latex]6\%[/latex] interest compounded monthly.
How much would you need to deposit in an account now in order to have [latex]$20,000[/latex] in the account in [latex]4[/latex] years? Assume the account earns [latex]5\%[/latex] interest.
You deposit [latex]$200[/latex] each month into an account earning [latex]3\%[/latex] interest compounded monthly.
How much will you have in the account in [latex]30[/latex] years?
How much total money will you put into the account?
How much total interest will you earn?
You deposit [latex]$1000[/latex] each year into an account earning [latex]8\%[/latex] compounded annually.
How much will you have in the account in [latex]10[/latex] years?
How much total money will you put into the account?
How much total interest will you earn?
Jose has determined he needs to have [latex]$800,000[/latex] for retirement in [latex]30[/latex] years. His account earns [latex]6\%[/latex] interest.
How much would you need to deposit in the account each month?
How much total money will you put into the account?
How much total interest will you earn?
You wish to have [latex]$3000[/latex] in [latex]2[/latex] years to buy a fancy new stereo system. How much should you deposit each quarter into an account paying [latex]8\%[/latex] compounded quarterly?
You want to be able to withdraw [latex]$30,000[/latex] each year for [latex]25[/latex] years. Your account earns 8% interest.
How much do you need in your account at the beginning
How much total money will you pull out of the account?
How much of that money is interest?
How much money will I need to have at retirement so I can withdraw [latex]$60,000[/latex] a year for [latex]20[/latex] years from an account earning [latex]8\%[/latex] compounded annually?
How much do you need in your account at the beginning
How much total money will you pull out of the account?
How much of that money is interest?
You have [latex]$500,000[/latex] saved for retirement. Your account earns [latex]6\%[/latex] interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for [latex]20[/latex] years?
Loren already knows that he will have [latex]$500,000[/latex] when he retires. If he sets up a payout annuity for [latex]30[/latex] years in an account paying [latex]10\%[/latex] interest, how much could the annuity provide each month?
You can afford a [latex]$700[/latex] per month mortgage payment. You’ve found a [latex]30[/latex] year loan at [latex]5\%[/latex] interest.
How big of a loan can you afford?
How much total money will you pay the loan company?
How much of that money is interest?
Marie can afford a [latex]$250[/latex] per month car payment. She’s found a [latex]5[/latex] year loan at [latex]7\%[/latex] interest.
How expensive of a car can she afford?
How much total money will she pay the loan company?
How much of that money is interest?
You want to buy a [latex]$25,000[/latex] car. The company is offering a [latex]2\%[/latex] interest rate for [latex]48[/latex] months ([latex]4[/latex] years). What will your monthly payments be?
You decide finance a [latex]$12,000[/latex] car at [latex]3\%[/latex] compounded monthly for [latex]4[/latex] years. What will your monthly payments be? How much interest will you pay over the life of the loan?
You want to buy a [latex]$200,000[/latex] home. You plan to pay [latex]10\%[/latex] as a down payment, and take out a [latex]30[/latex] year loan for the rest.
How much is the loan amount going to be?
What will your monthly payments be if the interest rate is [latex]5\%[/latex]?
What will your monthly payments be if the interest rate is [latex]6\%[/latex]?
Lynn bought a [latex]$300,000[/latex] house, paying [latex]10\%[/latex] down, and financing the rest at [latex]6\%[/latex] interest for [latex]30[/latex] years.
Find her monthly payments.
How much interest will she pay over the life of the loan?
Emile bought a car for [latex]$24,000[/latex] three years ago. The loan had a [latex]5[/latex] year term at [latex]3\%[/latex] interest rate. How much does he still owe on the car?
A friend bought a house [latex]15[/latex] years ago, taking out a [latex]$120,000[/latex] mortgage at [latex]6\%[/latex] for [latex]30[/latex] years. How much does she still owe on the mortgage?
Pat deposits [latex]$6,000[/latex] into an account earning [latex]4\%[/latex] compounded monthly. How long will it take the account to grow to [latex]$10,000[/latex]?
Kay is saving [latex]$200[/latex] a month into an account earning [latex]5\%[/latex] interest. How long will it take her to save [latex]$20,000[/latex]?
James has [latex]$3,000[/latex] in credit card debt, which charges [latex]14\%[/latex] interest. How long will it take to pay off the card if he makes the minimum payment of [latex]$60[/latex] a month?
Chris has saved [latex]$200,000[/latex] for retirement, and it is in an account earning [latex]6\%[/latex] interest. If she withdraws [latex]$3,000[/latex] a month, how long will the money last?
Concepts
Suppose you invest [latex]$50[/latex] a month for [latex]5[/latex] years into an account earning [latex]8\%[/latex] compounded monthly. After [latex]5[/latex] years, you leave the money, without making additional deposits, in the account for another [latex]25[/latex] years. How much will you have in the end?
Suppose you put off making investments for the first [latex]5[/latex] years, and instead made deposits of [latex]$50[/latex] a month for [latex]25[/latex] years into an account earning [latex]8\%[/latex] compounded monthly. How much will you have in the end?
Mike plans to make contributions to his retirement account for [latex]15[/latex] years. After the last contribution, he will start withdrawing [latex]$10,000[/latex] a quarter for [latex]10[/latex] years. Assuming Mike’s account earns [latex]8\%[/latex] compounded quarterly, how large must his quarterly contributions be during the first [latex]15[/latex] years, in order to accomplish his goal?
Kendra wants to be able to make withdrawals of [latex]$60,000[/latex] a year for [latex]30[/latex] years after retiring in [latex]35[/latex] years. How much will she have to save each year up until retirement if her account earns [latex]7\%[/latex] interest?
You have [latex]$2,000[/latex] to invest, and want it to grow to [latex]$3,000[/latex] in two years. What interest rate would you need to find to make this possible?
You have [latex]$5,000[/latex] to invest, and want it to grow to [latex]$20,000[/latex] in ten years. What interest rate would you need to find to make this possible?
You plan to save [latex]$600[/latex] a month for the next [latex]30[/latex] years for retirement. What interest rate would you need to have [latex]$1,000,000[/latex] at retirement?
You really want to buy a used car for [latex]$11,000[/latex], but can only afford [latex]$200[/latex] a month. What interest rate would you need to find to be able to afford the car, assuming the loan is for [latex]60[/latex] months?
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.
Explain the general method by which the loan works.
We will assume that we need to borrow [latex]$500[/latex] and that we will pay back the loan in [latex]14[/latex] 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.
If you cannot pay back the loan after [latex]14[/latex] days, you will need to get an extension for another [latex]14[/latex] days. Determine the fees for an extension, determine the total amount you will be paying for the now [latex]28[/latex] day loan, and compute the effective loan rate.
Suppose that [latex]10[/latex] years ago you bought a home for [latex]$110,000[/latex], paying [latex]10\%[/latex] as a down payment, and financing the rest at [latex]9\%[/latex] interest for [latex]30[/latex] years.
Let’s consider your existing mortgage:
How much money did you pay as your down payment?
How much money was your mortgage (loan) for?
What is your current monthly payment?
How much total interest will you pay over the life of the loan?
This year, you check your loan balance. 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 [latex]$88,536[/latex] left to pay on your loan. Your house is now valued at [latex]$150,000[/latex].
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.)
How much money have you paid to the loan company so far?
How much interest have you paid so far?
How much equity do you have in your home (equity is value minus remaining debt)
Since interest rates have dropped, you consider refinancing your mortgage at a lower [latex]6\%[/latex] rate.
If you took out a new [latex]30[/latex] year mortgage at [latex]6\%[/latex] for your remaining loan balance, what would your new monthly payments be?
How much interest will you pay over the life of the new loan?
Notice that if you refinance, you are going to be making payments on your home for another [latex]30[/latex] years. In addition to the [latex]10[/latex] years you’ve already been paying, that’s [latex]40[/latex] years total.
How much will you save each month because of the lower monthly payment?
How much total interest will you be paying (you need to consider the amount from [latex]2[/latex]c and [latex]3[/latex]b)
Does it make sense to refinance? (there isn’t a correct answer to this question. Just give your opinion and your reason)