Question 1085984: The future value of an annuity is R 24 000. the monthly annuity is R 1000 and the annuity period is 2 years, what is the nominal interest rate
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! using a financial calculator, you would do the following:
fv= 24000
pv = 0
pmt = 2000
n = 2 * 12 = 24
i% = monthly interest rate as a percent.
the rules for the calculator are:
interest rate per time period as a percent = annual interest rate as a percent divided by number of compounding periods per year.
number of time periods = number of years * number of compounding periods per year.
with monthly payments, the number of compounding periods per year is 12.
unless otherwise stated, payments are assumed to be made at the end of each month.
i used the following financial calculator.
https://arachnoid.com/finance/
i entered the following inputs.
present value = 0
future value = 24000
number of time periods = 24
payment = 1000
interest rate per time period as a percent = blank
number of time periods =24
payment at end of time period
the inputs look like this:
i select interest rate per time period.
the outputs look like this:
the solution is that the interest rate per time period as a percent = 0%
initially i thought something might be wrong, but then i realized that 24 monthly payments of 1000 will be equal to 24,000 at the end of the 24 month period, therefore the interest rate would be 0.
since the nominal interest rate per year is 12 times the interest rate per month, then the annual interest rate is 0%.
any interest rate greater than 0% will result in a future value greater than 24,000.
for example, assume the interest rate percent each month is .5%
that would be an annual interest rate of 6% divide by 12 = .5%.
the future value of 24 monthly investments of 1000 each would be equal to 25,431.
here's the inputs:
i then select fv and here's the outputs:
as you can see, the future value is more than 24 * 1000.
when you use this calculator, you enter interest rate as a percent, i.e. .5%.
if you do the same calculation using manual formulas, you enter interest rate as a decimal, i.e. .005.
solving for the rate by use of a manual formula is usually an iterative process.
i tried doing it by using the future value of an annuity formula but gave up as i got the unknown variable r on both sides of the equation and couldn't figure out how to isolate the r so i could solve for it manually.
i resorted to graphing 2 equations and finding the intersection of them.
i got the right answer, but it was was solved graphically as a system of equations.
in your problem, it could be solved logically because 24 monthly payments is equal to the future value of the loan making the monthly interest rate = 0% which makes the annual interest rate = 0% as well.
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