SOLUTION: A student borrrowed R80000 from smart bank and undertook to pay back the loan over 13 years. The student paid a scheduled monthly payments in debit order.
Interest rate of 3.25% p
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Question 1044931: A student borrrowed R80000 from smart bank and undertook to pay back the loan over 13 years. The student paid a scheduled monthly payments in debit order.
Interest rate of 3.25% per annum, compounded monthly.
He paid only 3%.
What amound will the student be owing the bank at the end of the loan period, as well as the monthly interest he had to pay during the 4 years he was enrolled at university
Formula:A=(1+i)n
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the printout of the excel worksheet that i used is shown below:
printout of excel worksheet used to solve this problem
the link above shows the result of the excel spreadeet analysis.
first i assumed 3% and required amount of the loan in time point 48.
then i calculated the payment required for that amount at 3%.
column headed 3% shows the amount of the loan in time point 48 and the remaining balance in time point 204.
column 204 is the 156th time point of the loan starting in time point 48 because 48 + 156 = 204.
you can see that the loan is fully paid off in time point 204.
you can also see that time point 204 overall is time point 156 of the loan period.
column headed 3.25% shows the amount of the loan in time point 48 and the remaining balance in time point 204.
in column titled 3%, the payment per month was 698.87.
in column titled 3.25%, the payment per month was $716.70
in the 3% colum and the 3.25% column, the remaining balance at the end of the 204th month was 0, as it should be since the payments on the loans were calculated to make the remaining balance of those loans 0 at the end of the loan period.
the column titled 3.25% with payment of 698.87 per month looked at the loan at 3.25% only it made payments based on what he actually paid rather than what was required.
at the end of the 48 month period, he owed 91090.2625 and not 90186.2417.
he made payments of 698.87 and not 716.70
this caused the number of months required to pay off the loan of 91090.2625 at 3.25% compounded monthly to be between 160 and 161.
in the 156th month, he still owed $3,455.66.
that, i believe, is the solution to your problem.
it's hard to explain, but i'm pretty sure this is what you are looking for.
the concept was:
find out the payments he needed to make if the loan was at 3%.
find out the payments he needs to make if the loan was at 3.25%.
assume the future value of the loan for 48 months was at 3.25% and the payments on the loan at 3.25% were 698.87 per month rather than 716.70 per month.
find the remaining balance at the end of 156 months.
check the printout at time point 48 and time point 204.
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