Question 1111110: Kim is planning to buy a new house worth $790000. She is required to pay a 30% deposit, and then borrow the rest at a flat interest rate. If Kim calculated that the monthly repayment over 20 years is $4192, find the interest rate, to 2 decimal places.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! as far as i know, flat interest is calculated up front off the principal and then the payments are calculated from that.
this is a different formula than compound interest and is calculated in a totally different way.
the house is worth 790,000.
she pays a 30% deposit, which is equal to 237,000
the balance that needs to be paid off is 790,000 - 237,000 = 553,000.
this is a 20 year loan whose monthly payments are 4192.
20 * 12 * 4192 equals total payments of 1,006,080.
she paid 1,006,080 minus 553,000 = 453,080 in interest on the loan over the 20 year period
the flat rate interest formula is i = p * i * n
p is the principal
i is the interest rate per time period
n is the number of time periods
this formula becomes 453,080 = 553,000 * i * 20
solve for i to get i = 453,080 / (553,000 * 20)
this makes i = .040965642 per year.
that's the flat rate interest rate of the loan.
the calculation of interest on the principal of the loan would have been:
i = p * r * n
p is 553,000
r is .040965642
n is 20
i = 553,000 * .040965642 * 20 = 453,080.
the total that needs to be paid back is 553,000 + 453,080 = 1,006,080
round the interest rate to 2 decimal places and it becomes .04.
that should be your solution.
note that interest rate and interest rate percent are two different things.
the interest rate is .040965642.
the interest rate is 100 times that = 4.0965642 %.
round the percent to 2 decimal places and it becomes 4.1%.
rounding to 2 decimal places, your answer is .04 interest rate, but 4.1% interest rate percent.
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