Question 1139233: Joseph bought a town house in Northriding, Johannesburg, for R700 000 in 2007. He paid a deposit of R100 000 and managed to secure a loan for the outstanding amount. The term of the loan was 20 years and the interest rate was fixed at 7,75% per year, compounded monthly. Calculate Joseph minimum monthly payment to the nearest cent. 1.) Consider the amortisation of Joseph loan above. What will the outstanding balance, to the nearest cent, on the loan be after 12 years minimum payments have been made? 2.) How much will the town house cost Joseph in total over 20 years, deposit included? 3.) Consider the amortisation of Joseph loan above. Suppose Joseph made all minimum monthly payments on time into his loan account. In which year and month will the principal that is paid off in that month for the first time be more than the interest paid off? 4.) Suppose Joseph decided to pay R6 000 per month into his loan account from the start. How many years would it take Joseph to pay off this loan?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Joseph bought a town house in Northriding, Johannesburg, for R700 000 in 2007. He paid a deposit of R100 000 and managed to secure a loan for the outstanding amount. The term of the loan was 20 years and the interest rate was fixed at 7.75% per year, compounded monthly.
Calculate Joseph minimum monthly payment to the nearest cent.
the monthly payment would be $4,925.69
1.) Consider the amortization of Joseph loan above. What will the outstanding balance, to the nearest cent, on the loan be after 12 years minimum payments have been made?
the outstanding balance at the end of the 12th year would be $351,585.39.
2.) How much will the town house cost Joseph in total over 20 years, deposit included?
the total cost would be 240 monthly payments of $4925.69135 = $1,182,165.93 plus $100,000 deposit = $2,282,165.93.
if you use the monthly payment rounded to the nearest penny, then the total cost would be 240 monthly payments of $4925.69 = $1,182,165.6 plus $100,000 deposit = $2,282,165.6.
the difference between using the monthly payment to the nearest penny and using the monthly payment before it was rounded is very small.
3.) Consider the amortization of Joseph loan above. Suppose Joseph made all minimum monthly payments on time into his loan account. In which year and month will the principal that is paid off in that month for the first time be more than the interest paid off?
the principal part of the payment would become greater than the interest part of the payment some time between the end of month 133 and the end of month 134.
that would be sometime between the end of the first month of the 11th year and the end of the second month of the 11th year.
4.) Suppose Joseph decided to pay R6,000 per month into his loan account from the start. How many years would it take Joseph to pay off this loan?
it would take joseph 161.239108 months to pay off the loan if he paid $6000 at the end of each month.
that would be sometime between the end of the 13th year and the end of the 14th year.
it would be 13 years and 5.259108 months.
this means sometime between the end of the fifth month and the end of the 6th month in the 13th year.
the following excel spreadsheet printouts show the detailed calculations in the pertinent months.
---------------- the first 3 show with monthly payments of $4925.69.
---------------- the next 3 show with monthly payments of $6000.00.
any questions, write to dtheophilis@gmail.com.
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