Take a Test-JEREL INEY JERELIVEY 1 2/1/18 2:57 Pm Quiz: Section 7.1-7.3 Quiz Sub
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Take a Test-JEREL INEY JERELIVEY 1 2/1/18 2:57 Pm Quiz: Section 7.1-7.3 Quiz Submit Qu This Question: 1 pt |4 of 14 (2 complete ) This Quiz: 20 pts possil Laura Kennedy needs to borrow $4995 to pay for NBA season tickets for her family She can borrow the amount from a finance company at 6 1% add-on interest for 3 years) or from the credit union (36 monthly payments of $161.17 each). Laura takes the credit union loan. At the time of her thirtieth payment she pays it off. If the credit union uses the rule of 78 for computing unearned interest, how much will she save by paying off the loan with the thirtieth payment? The amount that she will save by paying in full now is (Round to the nearest cent as needed)Explanation / Answer
The total interest the credit union would've earned from those 36 payments is : (161.17*36)-4995=807.12, let us denote this sum by S, therefore S=$807.12, therefore the interest rate under this setting is 5.386% p.a.
Under the rule of 78 we first add up the months for the note:(in this step we add the no. of month, i.e we add 1 for month 1, 2 for month 2 so on till 36 for month 36.)
1+2+3+4+5+.......+35+36=666. Let us denote this no. the sum of months by M=666.
Now since Laura paid the loan off in the 13th month, the amount the union would charge for early repayment is computed as follows:
807.12*(12/666)=15.755,
Thus the total amount paid by her in the final payment in month 13 is (let us denote this sum by T).
T = 4995-A+15.755,
where A is the part of the principal amount($4995) repaid in the 1st 12 months, which is given by:
A=161.17*12 - 4995*.05386=$1665
Therefore T = 3330+15.755= $3345.755.
The total amount paid including the payments in 1st 12 months is: T+161.17*12 = $5279.8
Thus the total amount she saved by paying the loan in the 13th month is 161.17*36-5279.8 = $522.32.
Therefore the answer is $522.32
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