Question 1138716: The Ram Company borrowed $20 000 at 10% compounded semi-annually and made payments toward the loan of $8000 after two years and $10 000 after three-and-a-half years. How much is required to pay off the loan one year after the second payment?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! they borrowed 20,000 at 10% compounded semi-annually.
the interest rate per half year time period was 10% / 2 = 5% / 100 = .05.
the number of half year periods was equal to 2 times the number of years.
they made payment of $8,000 at the end of 2 years and $10,000 at the end of 3.5 years.
the remaining balance on the loan started at 10,000.
at the end of 2 years after the loan was made, the remaining balance of the loan after interest was added but before payment was made was equal to $10,000 * 1.05 ^ 4 = $24,310.13.
they made their payment of $8,000 and the remaining balance on the loan after interest added and payment was subtracted was equal to $24,310.13 minus $8,000 = $16,310.13.
at the end of 3.5 years, which was 1.5 years after the end of 2 years, the remaining balance on the loan was $16,310.13 * 1.05 ^ 3 = $18,881.01 after interest was added but before payment was made.
they made their payment of $10,000 and the remaining balance on the loan after interest was added and payment was made became equal to $8,881.01.
one year after that, the remaining balance on the loan was 8,881.01 * 1.05 ^ 2 = 9,791.31.
that's your solution.
that's how much was required to pay off the loan one year after the last payment was made.
this can be seen in more detail in the following excel spreadsheet printout.
the formula used is f = p * (1 + r) ^ n
f is the future value
p is the present value
r is the interest rate per time period
n is the number of time periods.
the time period is in half years.
the rate per half year is 10% / 100 = .10 / 2 = .05 per half year.
the number of half years is 2 times the number of years.
1 + r becomes (1 + .05) which becomes 1.05.
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