Question 1129176: A loan for $5000 with interest at 7.75% compounded semi annually is reaid after 5years,10 months. What is the amount of interest paid
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'm not exactly sure how this is done, but i'll take a stab at it.
present value = 5000
interest rate = 7.75% every year / 2 = 3.875% every half year time period.
5 years 10 months is equal to 5.8333333.... years * 2 = 11.6666666.... half years time periods.
payments every half year time period = 0.
payments made at end or beginning of each half year tiem period doesn't matter since the payments every half year are equal to 0.
your inputs to the financial calculator are:
present value = -5000
future value = 0
number of time periods = 11.66666666... half years.
payment in each time period = 0
interest rate per time period = 7.75% / 2 = 3.875%
payment made at end or beginning of each time period doesn't matter since the payments in each time period = 0.
you click on fv and the calculator tells you that the future value is equal to 7791.10.
here's the display from the calculator.
i'm reasonably sure this is the way it's done.
if you find that the expected answer is not what i've shown you, let me know what the expected answer is and i'll try to figure out why it's not what i told you.
your nominal interest rate is 7.75% per year.
your effective interest rate is 7.75 / 2 = 3.875% every 6 months.
anything less than 6 months is calculated as (1.03875)^(x/6), where x is the number of months.
the manual formula is f = p * (1 + r) ^ n
f = what you want to find
p = 5000
r = 7.75%/100 = .0775/2 = .03875 per half year
n = 5 years and 10 months = 5.833..... years * 2 = 11.666.... half years.
the formula becomes f = 5000 * (1 + .03875) ^ 11.666.... = 7791.09979 = 7791.10 rounded to the nearest penny.
the calculator works on the percent interest rate.
the manual formula works on the interest rate.
interest rate = percent interest rate / 100.
percent interest rate = interest rate * 100.
send any questions regarding this to dtheophilis@gmail.com
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
A loan for $5000 with interest at 7.75% compounded semi annually is reaid after 5years,10 months. What is the amount of interest paid
This is a loan which leads me to believe that monthly payments were made. The monthly payment, based on a principal of $5,000, interest rate
of 7.75%, and term of 5 years, 10 months, or  , is: $540.84. Such a payment, over a  , comes to $6,309.75.
Therefore, 
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