Question

6 [12 pts.] 4.1#5: Working similar to the above, a fixed APR loan charges interest at the end of each cycle that is equal to the specified fixed percentage of what is currently owed. (a.) Use this idea to recursively define a sequence that models how much is owed upon a loan of $1000 that accrues 2% interest at the end of every month (24% APR-not too far different from that of many credit cards), and is paid off at a constant rate of $25 per month. (b.) Do the same for someone who paid a constant rate of $30 per month. (c.) Using a computer program like Excel, MATLAB, or Mathematica, compute how many months each of these people spent paying off their loans, as well as the total amount of interest paid. (This is found from taking subtracting the initial loan amount of $1000 from the product of the number of monthly payments with the amount of those monthly payments.) Hint: Part c. will likely be easiest to do by just computing the amount in the account each month until you get to a number smaller than the monthly payment.

Answer 1

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Calculation has been made using Excel.

Formula used shown against answers.

Answer Part A: Total payment of $2031.85 needs to be made during loan tenure of 81.27 months with EMI of $25

Answer Part B: Total payment of $1664.34 needs to be made during loan tenure of 55.48 months with EMI of $30

Answer Part C: 81.27 months to repay loan at $25 per month and 55.48 months to repay loan at $30 per month.

Bookl Microsoft Excel Home Insert Page Layout Formulas Data Review View Develope Cut Copy Σ AutoSum Sort& Find & Editing 田, Sa. ▲ =涅, glilerge & Center. S-% , 'al;o Conditional asomble. Styles. Insert Delete Format B 1 u = 2Clear FilterSelect Number Cells Alignment Styles ENPER(BA/B6,B5, B3) B8 Loan amount 4 Interest rate S Monthly payment 6 Compounding periods per year 1,000.00 24% 12 81.27 months Formula: NPER(B2/84,B3,-B1) Formula:-B6 B3 8 Periods 9 Total payment to be made (Total 2,031.85 11 PARTB 12 Loan amount 13 Interest rate 14 Monthly payment 15 Compounding periods peryear $1,000.00 24% $ 30.00 12 5.48 months Formula:NPER(B11/B13,B12,-B10) Formula:-B15*B12 17 Periods 18 Total payment to be made (Total 19 20 PART C 21 22 Total amount of interest paid in $25 EMI $1,031.85 23 s spent paying off $25 EMI months Formula:-B9-B3 Months spent paying off $30 EMI 55.48 months Formula:-B18-B12 14 4 ト커: Sheet1 Sheet2 Sheet3. Sheet4 Ready 100% l 10:35 AM

Note: EMI stands for Equated Monthly Installments.