e\"To purchase a new car, you borrow $34,000 for 10 years at the rate of interes

Question

e"To purchase a new car, you borrow $34,000 for 10 years at the rate of interest of 8.6% APR compounded monthly, and you make monthly car payments. How much interest do you pay on the 11th payment?"

f"Suzan is considering buying a home for $256,000. If she makes a down payment of $78,000 and takes out a mortgage on the rest of the money at 6.28% compounded monthly for 19 years, what will be the interest for payment number 114? Assume she makes monthly payments. "

g"If the nominal interest rate is 9.1% compounded daily, what is the required quarterly payment to repay a loan of $22,000 in 10 years? Assume 91 days per quarter."

Explanation / Answer

e.

Find the monthly payment

Periodic payment of a loan is given by

P = L[r(1 + r)^n]/[(1 + r)^n - 1]

P - Periodic payment = ?

r - Interst rate = 0.086/12 = 0.0071667

n - Term = 10*12 = 120

L - Loan amount = 34000

P = 34000[0.0071667(1 + 0.0071667)^120]/[(1 + 0.0071667)^120 - 1] = $423.37

Prepare the amortization table, as below for the first 11 payments

From the above table, interest component in 11th payment = $230.37

Year Balance at the beginning of period Total payment Amount to interest = Balance * 0.0071667 Amount to principal = Total payment - Amount to interest Ending Balance 1 34000 423.37 243.67 179.70 33820.30 2 33820.30 423.37 242.38 180.99 33639.30 3 33639.30 423.37 241.08 182.29 33457.01 4 33457.01 423.37 239.78 183.60 33273.42 5 33273.42 423.37 238.46 184.91 33088.51 6 33088.51 423.37 237.14 186.24 32902.27 7 32902.27 423.37 235.80 187.57 32714.70 8 32714.70 423.37 234.46 188.92 32525.78 9 32525.78 423.37 233.10 190.27 32335.52 10 32335.52 423.37 231.74 191.63 32143.88 11 32143.88 423.37 230.37 193.01 31950.88

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