# 2010-01-30_183334_JA118_tjdouglas

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```					Simon recently received a credit card with an 18% nominal interest rate. With the
card, he purchased new stereo for \$350. The minimum payment on the card is only \$10
per month.
a. If Simon makes the minimum monthly payment and makes no other charges, how many
months will it be before he pays off the card? Round to the nearest month.
b. If Simon makes monthly payments of \$30, how many months will it be before he
pays off the debt? Round to the nearest month.
c. How much more in total payments will Simon make under the \$10-a - month plan
than under the \$30-a-month plan? Make sure you use three decimal places for N.

The relationship between the loan amount, periodic payments, interest rate, and
number of payments for such annuities is given as:

     1            
1
 (1  r ) n       
A  P                  
   r                                        (1)

                  

where A is the loan amount, P is the periodic (e.g. monthly) payment, r is the
effective interest rate, and n is the number of periods.

a) To find how long it will take Simon to pay off the loan we need to write
equation (1) with n as the dependent variable (i.e. the quantity on the left hand
side of the equation should be n). This can be done as:

    Ar 
 log 1      
n            P 
log(1  r )                                (2)

In this case A = 350, r = 18%/12 = 0.015, P = 10. Substituting these numbers into
(2) gives n = 50.
Thus it will take Simon 50 months to pay off the \$350 credit card debt.

b) Similar to part (a), but this time P = 30. Using equation (2) again we get n =
12.9 or 13 months to pay off the debt.

c) In the \$10 a month plan Simon will pay a total of 10 x 50 = \$500.
In the \$30 a month plan Simon will pay a total of 30 x 13 = \$390.
Thus under the first plan Simon ends up paying \$500 - \$390 = \$110 more.

```
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