a) The Sarkozy family buys a house for $300,000 with a down payment of $40,000.
ID: 3038047 • Letter: A
Question
a) The Sarkozy family buys a house for $300,000 with a down payment of $40,000. They take out a 30-year mortgage loan for $260,000 at an annual rate of interest of 4.8% compounded monthly. i) What is the monthly payment? ii) What is the total interest paid by the Sanchez family to the lender? iii) What is the amount of interest in the first payment? iv) What is the outstanding balance after 15 years? b) Sonia wants to buy a sports car selling for $90,000. The dealer offers her to sell the car if she agrees to pay $2200 at the end of every month for five years. What is the rate of interest compounded monthly being charged by the dealer? c) Jane borrows s 10,000 at the rate of interest of 5% compounded annually. She can pay $ 1200 at the end of every year for as long as necessary. What is the number of payments. (Don't worry if your answer is a fractional number.)Explanation / Answer
8. (a)
(i) The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is P = L[r(1 + r)n]/[(1 + r)n -1 ]. Here, r = 0.048/12 = 0.004. n = 12*30 = 360 and L = $ 260000. Hence P = 260000[ 0.004(1.004)360]/[(1.004)360 -1] = 1040 *(4.208589926)/ (3. 208589926) = $1364.13 ( on rounding off to the nearest cent).
(ii) The amount paid back to the bank is 360*$1364.13 = $ 491086.80. Therefore, the interest paid to the Bank by the Sarkozy/ Sanchez family is $ 491086.80- $ 260000 = $ 231086.80.
(iii) The 1st payment will consist of interest of $ 260000* 4.8 %/12 = $1040 and principal of $ 1364.13-$ 1040 = $ 324.13.
(iv). The formula used to calculate the remaining loan balance (B) of a mortgage loan after p months is B = L[(1 + r)n - (1 + r)p]/[(1 + r)n -1]. Here, the remaining loan balance from a mortgage loan of $ 260000, after 15 years is B = 260000[ (1.004)360 –(1.004)15*12]/ [(1.004)360 -1] = 260000(4.208589926-2.05148481) /(3. 208589926) = 260000(2.1571051160/(3. 208589926) = $ 174795.58(on rounding off to the nearest cent).
Please post the parts (b) and (c) again separately.
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