INSTANT MONEY 1

Instant Money

Mrinalini Sugosh and Megan Wenzlaff

Lakeshore High School – 11/19/12

INSTANT MONEY 2

Introduction

The advertisement ‘Instant Money’ is offering a loan with low monthly

payments. A loan is where a lender gives money to a borrower, expecting

the money to get paid off during a set amount of time with interest. Interest

is an additional payment on a loan, given in a percent that offers. To pay off

a loan, people make payments. These payments have interest added to

them, which can be collected annually, quarterly, monthly, or weekly. In this

advertisement, people can get as much as $5000 and pay a mere 2% of the

loan’s balance. Despite no fees, it contains a 21.9% annual interest rate that

is compounded monthly. The offer suggests it is a cheap, convenient loan,

with monthly payments that decrease, implying that the loan is better than

others. However, the research suggests otherwise. Although a person pays a

small amount, the length of time it takes for the loan to dissipate outweighs

any benefits it brings. In the end, they pay more money because they have

to have more payments over a longer period of time.

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Calculations and Results

Loan Balance

starting value of loan

We got the recursive formula from the following:

[(

) ]

Product Prior Interest Monthly

Value Rate Payment Rate

is the loan balance. This is derived from the prior loan balance, , times

the annual interest rate compounded monthly. This is represented as,

. Then, you have to subtract the ‘low monthly payment’ of 2%.

Therefore, the final equation to find the loan balance is

[(

) ].

Monthly Payments

starting value of loan

We got the recursive formula from the following:

Monthly Starting Monthly

Payment Value Payment Rate

is the monthly payment amount. This is derived from the monthly

payment from the previous month, . To get the monthly payment, you

times it by .02, which is the 2% monthly payment rate of the loan.

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Cumulative Payments

starting value of loan

We got the explict formula from the following:

∑

∑

The first formula shows that sum once the loan is paid off, or the cumulative

payment. 5000 is the starting value of the loan while .9983 is the decay

rate. To find this, you solve the rate in the loan balance as shown in the box

above. You then multiply the rate by the monthly payment which is .02. This

distributes out and gives the total amount that will be paid altogether.

The second formula shows the same equation just simplified. 5000 divided

by .02 gives you 100. You multiply it by rate of decay to the power,

giving you the cumulative sum.

[(

) ]

[ ]

Rate of decay

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INSTANT MONEY 6

Graph

The data table (on p.5) and graph represents the amount of money

paid throughout the months with the loan, and how much money is left on

the loan. As you can see in the highlighted sections, the loan’s balance

decreases at a very slow rate, compared to the cumulative total, which

increases rapidly in comparison. Over a 106 month period, the loan balance

only went to approximately $4,100. The cumulative payment, however, went

to about $10,000. This shows a strong discrepancy between the amounts

paid versus the amount left on the loan. Another point that showcases this is

that after 52 months, it is clear from the graph that you’ve paid off $5,000.

Despite this, the loan balance is at a very high amount still, roughly $4,600.

-

2,000.00

4,000.00

6,000.00

8,000.00

10,000.00

12,000.00

1 6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96

10

1

10

6

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y

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D

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s)

Months

Instant Money Scam

CummulativePayment

Loan Balance

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Conclusion

Overall, the loan is a very bad investment, and the total amount paid

far surpasses the amount seemingly saved with the low monthly payments.

At 52 months, or approximately 4 years and 4 months, you’ve paid a

cumulative sum of about $5,000. However, with the low interest fees and

payment rate, you still owe around $4,500 dollars. That means only $500 of

the $5000 paid actually went to decreasing the loan’s value. The loan stops

after 250 to 350 years, but the calculator is unable to calculate beyond 2771

months or 230 years. However, calculating things off manually indicates that

by about 300 years, the loan is fully paid off. In this time period, over

$60,000 went into paying a mere $5,000 loan. Therefore, scams such as

‘Instant Money’ are very pricy and must be carefully analyzed.

INSTANT MONEY 8

References

Landeck, K. (2012, November 18). Instant Money Project Handout. In

Lakeshore Math 2012-2013. Retrieved November 18, 2012, from

http://lakeshoremath.weebly.com/uploads/4/5/8/7/4587368/11_assig

nment_sheet_calculator_notes.pdf

Murdock, J., Kamischke, E., & Kamischke, E. (2004). Discovering

Advanced Algebra - An Investigative Approach (pp. 28-67 & pp. 630-

650). Emeryville, CA: Key Curriculum Press.