Question 1134284
this is best done using a financial calculator.


one that i use online can be found at <a href = "https://arachnoid.com/finance/" target = "_blank">https://arachnoid.com/finance/</a>


the problem doesn't say whether the payments are monthly or yearly.


they are usualy monthly so i'll do that first.


the present value of the loan is 195,000.
the future value of the loan needs to be equal to 0 once it's all paid off.
the number of time periods of the loan is 25 years * 12 months per year = 300 months.
the interest rate per time period is 8.25% per year / 12 months per year = .6875% per month.
the payments are assumed to be made at the end of each month.


input these values into the calculator and click on PMT and the calculator tells you that the payments at the end of each month need to be equal to 1,537.48.


to find the amount of interest paid, multiply the monthly payments by 300 and subtrsact the initial value of the loan to get 1537.48 * 300 = 461,244 minus 195,000 = 266,244.


that's how much interest was paid over the 25 year period if the payments were made at the end of each month.


i used a financial calculator off line to do the same thing.
this calculator doesn't round the results.
the calculator said that the monthly payments needed to be 1,537.477763.
multiply those by 300 to get total payments of 461,243.3288
subtract 195,000 to get total interest of 266,243.3288.
round to two decimal places to get total interest of 266,243.33.


the rounded monthly payments of the online calculator yielded total interest of 266,244.
the unrounded monthly payments of the offline calculator yielded total interest of 266,243.33.


the more correct figure would be from the offline calculator.
the error factor is quite small.
your solution may be one or the other depending on what your instructor expects you to do.


the above calculations assume monthly payments.


yearly payments would give you a different answer.


with end of year payments, the inputs to the calculator will be.


present value = 195,000
interest rate per year = 8.25%
number of years = 25.
payment are made at the end of each year.


online calculator will tell you that the payments at the end of each year need to be 18,659.03


offline calculator will tell you that the payments at the end of each year need to be 18,659.02892


total interest from online calculator results will be 18,659.03 * 25 = 466,475.75 minus 195,000 = 271,475.75.


total interest from offline calculator results will be 18,659.02892 * 25 = 466,475.7229 minus 195,000 = 271,475.7229 = 271,475.72 rounded to two decimal places.


one of those answers should be the one your are looking for depending on how your instructor expects you to round.


here are the results fromt the use of the online calculator.


first the monthly payments.


then the yearly payments.


total interest is monthly payment * 300 minus 195,000.


total interest is yearly payment * 25 minus 195,000.


<img src = "http://theo.x10hosting.com/2019/020703.jpg" alt="$$$" >


<img src = "http://theo.x10hosting.com/2019/020704.jpg" alt="$$$" >


the offline calculator i used is the Texas Instruments Business Analyst 2.


this is sometimes shown as HP BA II.