Jan sold her house on December 31 and took a $35,000 mortgage as part of the payment. The 10-year mortgage has a 8% nominal inte
rest rate, but it calls for semiannual payments beginning next June 30. Next year Jan must report on Schedule B of her IRS Form 1040 the amount of interest that was included in the two payments she received during the year.
a. What is the dollar amount of each payment Jan receives? Round your answer to the nearest cent.
b. How much interest was included in the first payment? Round your answer to the nearest cent.
c. How much repayment of principal was included? Round your answer to the nearest cent.
d. How do these values change for the second payment?
a. What is the dollar amount of each payment Jan receives? Round your answer to the nearest cent.
b. How much interest was included in the first payment? Round your answer to the nearest cent.
c. How much repayment of principal was included? Round your answer to the nearest cent.
d. How do these values change for the second payment?
1 answer:
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Answer:
(a)
(b)
(c) X=4.975 percent
Explanation:
(a) Find the z-value that corresponds to 5.40 percent
.
Hence the net interest margin of 5.40 percent is 2.5 standard deviation above the mean.
The area to the left of 2.5 from the standard normal distribution table is 0.9938.The probability that a randomly selected U.S. bank will have a net interest margin that exceeds 5.40 percent is 1-0.9938=0.0062
(b) The z-value that corresponds to 4.40 percent is The net interest margin of 4.40 percent is 0.5 standard deviation above the mean.
Using the normal distribution table, the area under the curve to the left of 0.5 is 0.6915
Therefore the probability that a randomly selected U.S. bank will have a net interest margin less than 4.40 percent is 0.6915
(c) The z-value that corresponds to 95% which is 1.65
We substitute the 1.65 into the formula and solve for X.
A bank that wants its net interest margin to be less than the net interest margins of 95 percent of all U.S. banks should set its net interest margin to 4.975 percent.
