SOLUTION: The table of conversion from flat interest rate to reducing balance interest rate is based on the formula F= (1+R)^n (nR-1)+1/ n(1+R)^n-n, where F is the flat rate per month, R is

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: The table of conversion from flat interest rate to reducing balance interest rate is based on the formula F= (1+R)^n (nR-1)+1/ n(1+R)^n-n, where F is the flat rate per month, R is       Log On


   

Question 1178363: The table of conversion from flat interest rate to reducing balance interest rate is based on the formula F= (1+R)^n (nR-1)+1/ n(1+R)^n-n, where F is the flat rate per month, R is the reducible rate per month and n is the number of monthly payments. To get the monthly rate, divide the annual rate by 12. Calculate the approximate flat interest rate for 8% per annum reducible for 3 years.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
F= (1+R)^n (nR-1)+1/ n(1+R)^n-n.
F is the flat rate per month, R is the reducible rate per month and n is the number of monthly payments.

i don't know about that formula.
i wasn't able to duplicate my answer with it.
what i did do is the following:

i used a financial calculator to get the payment for reducing balance at 8% per month for 36 monhs, using a starting balance of 1000.

that monthly payment was 31.33636546.

multiply that by 36 months and the the sum of the payments was 1128.109157.

subtract 1 from that to get sum of all interest payments = 128.109157.

the flat rate formula is i = p * r * t
i is the interest
p is the principal
r is the interest rate per time period
t is the number of time periods.

with i = 128.109157 and p = 1000 and t = 36, the formula becomes:
128.109157 = 1000 * r * 36
solve for r to get:
r = 128.109157 / (1000 * 36) = .003558588.
multiply that by 12 to get .042703052.

that's = to 4.2703052%.

what this says is that a flat rate of 4.2703052% per year is equivalent to a reducing balance rate of 8% per year compounded monthly.

what this is comparing is the interest from the flat rate loan to the interest from the reducing balance loan.

they will both charge the same overall interest with those rates.

i found a calculator online that does a comparison and that calculator confirms that i did the calculations correctly.\

here's what the results from that calculator looked like.





this is the best i can do.

i tried to use the formula but am not sure if i interpreted it correctly.

the method should work regardless of what the amount of the loan is.

the online reducing balance calculator i used is at https://arachnoid.com/finance/index.html

the results from use of that calculator are shown below:



i used the ti-ba-ii which gave me the more detailed answer with more decimal places.

the flat rate versus reducing balance calculator can be found at https://emi-calc.com/flat-rate-vs-reducing-balance-rate-emi-calculation.php