MAT 143 Midterm

Define the variables in the compound interest formula for interest paid more than once a year.

A is the accumulated balance after Y years, P is the stating principal, APR is the annual percentage rate, n is the number of compounding periods per year, and Y is the number of years.

State the compound interest formula for interest paid more than once a year.

A=P(1+APR/n)^(nY)

Explain why the term APR/n appears in the compound interest formula for interest paid n times a year.

APR represents the annual percentage rate. To account for the interest paid n times a year, this annual rate needs to be divided by the number of compounding periods per year n.

Distinguish between absolute and relative difference.

Absolute difference is the actual difference between the compared value and the reference value. Relative difference the size of the absolute difference in comparison to the reference value and can be expressed as a percentage.

How does Jefferson's method apportions seats.

Begin by finding the standard divisor, standard quotas, and minimum quotas. If there are extra seats, than choose a lower modified divisor and compute modified quotas. Round the modified quotas down to find a new set of minimum quotas. If there are extra seats, start again with a lower modified divisor. If there are not enough seats, start again with a higher modified divisor.

What is continuous compounding? How does the APY for continuous compounding compare to the APY for, say, daily compounding? Explain the formula for continuous compounding.

Compounding infinitely many times per year is called continuous compounding. The APY for continuous compounding is only slightly larger than the APY for daily compounding. The formula for continuous compounding is a special form of the compound interest formula.

How does Hamilton's method apportions seats.

First gave each state the number of seats found by rounding its standard quota down. If there are any extra seats, give one each of the extra seats to the states with the highest fractional remainders, until all seats are gone.

Briefly describe this history of Hamilton's method.

In 1792 President George Washington vetoed a bill authorizing Hamilton's method of apportionment. It was reintroduced and adopted as the apportionment procedure in 1850, and it remained in use until 1900.

Potions of loan payments going to principal and interest change over the life of the loan.

Installment loans gradually pay down the loan principal while the payments remain the same. Therefore, the interest due each month gradually decreases and the amount paid toward the principal gradually increases.

Briefly describe this history of Jefferson's method.

Jefferson's method of apportionment was the apportionment procedure from 1792 until the end of the 1830s, but it was abandoned after the 1840 Census.

What is the difference between simple interest and compound interest? Why do you end up with more money with compound interest?

Simple interest is interest paid only on the original investment whereas compound interest is interest paid both on the original investment and on all interest that has been added to the original investment. Since compound interest is calculated based on a larger amount than simple interest, it results in a larger amount of money over time.