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Help with Credit and Loans Practice test questions

1. Lynn had a $2,000 personal loan at 9.5 % for 18 months. Suppose that she is given the choice between the level method and the rule of 78 method and that she wants to pay off the remaining balance after a year of making monthly payments. Which method would she choose, and what difference in interest would she pay?
 
2. How long will it take Kate to pay for her furniture set if she chooses to pay only the minimum monthly payment of 2% of the outstanding balance? Her furniture set cost $3,750 financed at 19.75% annual interest.
 
3. Calculate the average daily balance (ADB) and the finance charge on Drew’s account that has 9.5% APR and a 30-day billing cycle. His January statement shows:
$425.89 balance carried from December
$133.15 K-Mart charge on January 5
$76.95 Greek Cuisine restaurant charge on January 8
$150.00 payment paid on January 10
$25.25 Texaco gas charge on January 11
$33.15 Target charge on January 21
$80.00 health club charge on January 26
$17.85 Wal-Mart charge on January 28
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1 Answer

Question One:
Best method to use is the level method.
Why?
1. 78 Rule method:
For a 18 months  term loan, the 78 rule factor will be nx(n+1)/2 for denominator and n for numerator where n is number of month in the loan. 
Thus the factor will be 18/171.
I the borrower pays off the loan after 12 months, interest will apply to the first 12 months. The interest paid will be 18/171 of total interest for the first month, 17/171 of total interest for the second month, 16/171 for the third, etc.... till 7/171 for the 12th month.
We know that total interest would have been 9.5% of $2,000: $190.
Applying the rule 78 factors to that total interest, after one year, interest paid would be $166.6
 
2. Level method:
Using the level method, interest per month would have been $190 divided by 18, $10.555 per month.  After 12 month, total interest paid would have been $10.555 X 12 = 126.6
 
Using the level method would have saved Lynn $40.
 
Question 2
APR is 19.75% equivalent to 1.6% per month.
Repayment is 2% of outstanding balance.
The loan is increasing by 1.6% due to interest and decreasing by 2% due to repayment.
Interest and repayment combined, the loan is decreasing by 0.4% each month.
It would take roughly 360 years to bring the outstanding loan to zero.
The maths behind my answer:
C: Outstanding loan: 3750
R: Repayment: 2%
I: Interest: 1.6%
D: Decrease factor : 1-(R-I) : 99.6%
n: number of months
N: number of years
Formula  :  CxD^n = 0. This is the equation to solve.  Using "what if" scenario with Excel , we can easily find the answer is N=360 (approximation)years.
 
Question 3
1. Calculating the billing cycle ADB:
    . carried over balance of 425.89 for 4 days thus 425.89 x 4 = 1,703.56
    . on the 5th, new balance of 559.04 for 3 days thus 559.04 x 3 = 1,677.12
    . on the 8th, new balance of 635.99 for 2 days thus 1,271.98
    . on the 10th, new balance of 485.99 for 1 day thus 485.99
    . on the 11th, new balance of 511.24 for 10 days thus 5,112.4
    . on the 21st, new balance of 544.39 for 5 days thus 2,721.95
    . on the 26th, new balance of 624.39 for 2 days thus 1,248.78
    . on the 28th, new balance of 642.24 for 3 days thus 1,926.72
Adding these number will give us a total of 16,148.5 for 30 days giving us a daily average of 16,148.5 divided by 30 = $538.28
2. Interest rate to apply
APR is 9.5%
30 days cycle rate will be  30/365*9.5% = 0.78%
3. Credit card cycle charge
ADB x 0.78% = 538.28 x 0.78% = $ 4.20
 

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