Question 1

If interest is compounded more than once a year, the annual percentage rate is also the effective interest rate.

Accepted Answer

When interest is compounded more than once a year, the effective interest rate is higher than the annual percentage rate.

Question 2

The nominal rate or stated rate is also referred to as annual percentage rate (APR).

Accepted Answer

The nominal rate or stated rate is also referred to as the annual percentage rate (APR).

Question 3

The nominal rate or stated rate is also referred to as effective annual rate (EAR).

Accepted Answer

The nominal rate or stated rate is not the same as the effective annual rate (EAR). The nominal rate is the interest rate stated on a loan or investment agreement, while the EAR takes into account the effect of compounding within a year.

Question 4

Continuous compounding is going to lead to the smallest difference between the effective annual rate (EAR) and annual percentage rate (APR).

Accepted Answer

Continuous compounding leads to the highest effective annual rate (EAR) when compared to the nominal annual percentage rate (APR), due to the principle of earning interest on interest more frequently.

Question 5

The effective annual rate on an account that pays 5% interest, compounded quarterly, is greater than the effective annual rate on an account that pays 4.8% interest, compounded continuously.

Accepted Answer

The effective annual rate (EAR) for an account that pays 5% interest, compounded quarterly, is calculated using the formula $EAR = (1 + \frac{r}{n})^n - 1$, where $r$ is the annual interest rate and $n$ is the number of compounding periods per year. For 5% interest compounded quarterly, this gives $EAR = (1 + \frac{0.05}{4})^4 - 1 = 1.050945\% $. For an account with 4.8% interest compounded continuously, the EAR is calculated using $EAR = e^r - 1$, where $e$ is the base of the natural logarithm, approximately equal to 2.71828, and $r$ is the annual interest rate. This gives $EAR = e^{0.048} - 1 = 4.911123\%$. Comparing these, the EAR for the 5% compounded quarterly is indeed greater than the 4.8% compounded continuously.

Question 6

The effective annual rate on an account that pays 10% interest, compounded semiannually, is greater than the effective annual rate on an account that pays 9.9% interest, compounded continuously.

Accepted Answer

The answer of The effective annual rate on an account...

Question 7

A loan, usually for real estate, that involves level, periodic payments consisting of interest and principal repayment over a specified payment period is best described as a mortgage.

Accepted Answer

A mortgage is indeed a type of loan specifically designed for the purchase of real estate, characterized by regular payments that include both principal and interest over a set period until the full loan amount is repaid.

Question 8

A monthly payment is the payment that represents repayment of some amount of the principal of the loan above and beyond what is paid as part of the amortized loan payments.

Accepted Answer

A monthly payment typically includes both the repayment of the principal of the loan and the interest, as part of the amortized loan payments, not above and beyond them.

Question 9

Suppose a homeowner is evaluating two mortgages, both of which are arrangements for repaying a loan of $200,000. Mortgage A requires quarterly payments at the end of each quarter for 15 years at a stated annual rate of 5%. Mortgage B has quarterly payments, paid at the beginning of each quarter for 18 years, at a stated annual rate of 5.5%. Mortgage A has a higher periodic payment than Mortgage

Accepted Answer

Mortgage A, with a shorter term and the same interest rate basis (quarterly), will have higher periodic payments than Mortgage B, despite Mortgage B's slightly higher interest rate, because the loan is amortized over a shorter period.

Question 10

Suppose a homeowner is evaluating two mortgages, both of which are arrangements for repaying a loan of $200,000. Mortgage C requires monthly payments at the end of each month for 15 years at a stated annual rate of 6%. Mortgage D has monthly payments, paid at the beginning of each month for 18 years, at a stated annual rate of 5.5%. Mortgage C has a higher periodic payment than Mortgage

Accepted Answer

The answer of Suppose a homeowner is evaluating two mortgages,...

Question 11

Suppose a company borrows $1 million and pays off this 10-year, 5% interest loan in end-of-year payments of $113,603.66 each. This loan is fully amortized at the end of the ten years.

Accepted Answer

The answer of Suppose a company borrows $1 million and...

Question 12

A company that borrows $10 million and pays this off with a 10-year, 5% interest loan in end-of-year payments of $1,295,045.75 each has a zero balance remaining on this loan at the end of 10 years.

Accepted Answer

The payments described are consistent with an amortizing loan where the borrower pays off the principal and interest over a set period, in this case, 10 years, with a fixed annual payment. The amount specified is calculated to ensure the loan is fully paid off, including interest, by the end of the term.

Question 13

If you deposit $5,000 in an account that pays 3% interest, compounded annually, what balance would you have at the end of four year?

Accepted Answer

The answer of If you deposit $5,000 in an account...

Question 14

What is the future value of $3,000 five years from now if interest is earned at a rate of 4% per year?

Accepted Answer

The answer of What is the future value of $3,000...

Question 15

What is the present value of $5,000 to be received five years from now if the discount rate is 6% per year?

Accepted Answer

The answer of What is the present value of $5,000...

Question 16

An investor invests $25,000 today for a five-year term and receives 4% annual compound interest.
A. How much would the investor have after five years?
B. How much interest-on-interest would the investor earn during the five years?

Accepted Answer

The answer of An investor invests $25,000 today for a...

Question 17

An investor invests $10,000 today for a four-year term and receives 5% annual compound interest.
A. How much would the investor have after four years?
B. How much interest-on-interest would the investor earn during the four years?

Accepted Answer

The answer of An investor invests $10,000 today for a...

Question 18

Suppose you are considering an investment that promises $25,000 in five years. If you determine that the appropriate discount rate for this investment, considering its risk, is 8%, what is this investment worth to you today?

Accepted Answer

The answer of Suppose you are considering an investment that...

Question 19

A friend's broker promises that they will double their money in five years with Investment

Accepted Answer

The answer of A friend's broker promises that they will...

Question 20

Complete the following table:

Accepted Answer

The answer of Complete the following table:
 ...

Quiz 5: Time Value of Money