interest rate

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MATH100: Mathematical Thinking Ch10: Mathematics of Money

REVIEW

Given the present value of money P, how do we find the future value of money F (and vice versa)?

One time payment/loan – lump sum: − E.g., I give you $1000 now, for 1 year, and I only hear from you one year from now when you

give me back the $1000 plus whatever interest we agreed upon!

Simple Interest

F = P(1+rt) Compounded Interest

F=P(1+r)t

F = future value; P = present value (principal); r = periodic interest rate; t = time of investment;

APR stands for the 'annual percentage rate'! If your investment/loan is compounded more than once a year, you must adjust the APR to the rate per period (in decimal form!), and include the correct number of periods : yearly: r = APR, t; monthly: r = APR/12, tx12; daily: r = APR/365, tx365.

Fixed annuities - equal payments made over regular time intervals − E.g., I give you $1000 now, for 1 year, under the condition that each month until the end of the

year, you will pay me a portion of the loan plus whatever interest we agreed upon!

Investments, Deferred Annuities

(Trust funds, Retirement accounts)

Installment Loans, Amortization,

(Loans, Mortgages)

Pay now, collect later! Pain (payments) comes first and the reward (a lump-sum payout) comes in the future!

Collect not, pay later! Reward (car, house, etc) comes first, and the pain (payment) is stretched out in to the future!

F = future lump-sum payout; P = present payments;

r = periodic interest rate; t = time of investment;

P = present amount of the loan; F = future payments;

r = periodic interest rate; t = time of investment;

Remember, given any three of the four variables in the formulas above, you can find the forth one using the formulas!

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MATH100: Mathematical Thinking Ch10: Mathematics of Money

Test Chapter 10 (10 points)

1. [1 point] The university charges an annual room and board fee of $4070 for a 10 Meal Plan. You choose the deluxe meal program, so your room and board is increased by 12.04%. What will be your increased room and board fee?

2. [1 point] An electronic store purchases a certain video game from the manufacturer for $10 per unit. The store sells the game at a nark-up of 80% over the purchase price. You found a coupon, offered in the local newspaper, which will reduce the price by 10%. How much money would the store profit if you purchased the video game using this coupon?

3. [1 point] The local Get-You-New-Computer-Here store offers you the following plan to purchase a new desktop set. The set retails for $2350, but you will have two years to pay for it using a simple interest loan. If you end up paying back $2560 after two years, then what is the APR on this loan?

4. [1 point] After several weeks of hard work you’ve made quite a bit of money during one summer break. You deposit the money into a savings account which offers an APR of 5 ¾ % compounded monthly. You forget about the account and five years later find that it contains $5000. How much money did you originally deposit into the account?

5. [1 point] A crowd gathered outside the electronics store big sign in the window: SALE! 20% OFF! Jim: “Not bad, everything is discounted 20%.” Mike: “Yes, but I came by here last week and they had just raised the prices by 20%. So there’s really no sale. We’re back where we started.” Bill: “No, there really is a sale. The final price is a bit lower than it was before the prices were raised.” Who is right?!

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Can you afford all these?! [use for questions 6 to 10]: You are successfully out of college for couple of years now, got the job of your dreams, married your soul mate, and just found out you are going to be a parent next month! Could not be a better time to plan your finances. You plan to buy a new house (You cannot wait to start decorating that baby room!), invest in some retirement account (After all, do you want to raise your kids just to have to take care of you because you never saved for retirement?), and maybe think about little one’s future education (You don’t want to seem selfish in that you are only taking care of you while putting your kid’s future needs aside!). Well, the question is, can you afford all these?!

6. [1 point] Assume that, in total, both of you make $100k/annually. Let's also assume that after tax and all other deductions (health insurance, Social Security, etc), you collectively take home about 72%. What is your monthly family income?

7. [1 point] First thing first (you've heard that if you want to save money you better start early!), you decide to open a college fund for your kid, from the day he or she is born until he or she turns 18. You are looking to secure $75k, so your kid won’t have to apply for extra loans when the time comes. How much should you contribute to a 6% APR college fund monthly, in order to accumulate 75k at the end of those 18 years?

8. [1 point] Second, you got your eyes on this nice 250k house, and you want to move in as soon as possible. Assuming you have no money for the down payment, you are basically looking at a 250k loan over the next 30 years. Calculate your monthly mortgage payment over the next 30 years, assuming a 4.5% APR interest rate.

9. [1 point] And finally, to care for retirement, you both decide to invest into separate Individual Retirement Accounts (IRA), each of you transferring same amount monthly to an IRA account, planning on cashing in 40 years later. IRA interest rates are usually pretty low, let's assume a 1% APR compounded monthly. Calculate how much money you will have to deposit monthly, each of you, if you want to cash at least 200k each from the IRA 40 years later.

10. [1 point] Given your monthly income and spending, can your family afford to buy a 250k house, to open a college trust fund worth 75k in 18 years, while also contributing monthly to the retirement accounts?

Salary +

Utilities -

Food -

Eating out, recreation, haircuts, etc. -

Cell phone -

Vacations -

Health Insurance -

House (mortgage) -

College Trust Fund -

Retirement Accounts (two of them) -

Balance