Question 1

Which of the following statements is false?

Accepted Answer

The answer of Which of the following statements is false?
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Question 2

A hospital received a contribution to its endowment fund of $2 million. The hospital can never touch the principal, but it can use the earnings. At an assumed interest rate of 9.5 percent, how much can the hospital earn to help its operations each year?

Accepted Answer

To calculate the annual earnings, we simply multiply the principal ($2 million) by the interest rate (9.5% or 0.095):

$2,000,000 x 0.095 = $190,000

Therefore, the hospital can earn $190,000 each year to help its operations.

Question 3

A loan that is repaid in equal payments over a specified time period is referred to as a(n):

Accepted Answer

An amortized loan is a loan that is repaid in equal payments over a specified time period. The payments are structured so that a portion of each payment goes towards interest and a portion goes towards paying down the principal balance. This means that the loan will gradually be paid off over time, with each payment bringing the borrower closer to being debt-free. Discounted loans, simple interest-free loans, and inflation-indexed loans all have different repayment structures and are not structured in the same way as amortized loans.

Question 4

Which of the following characteristics is not descriptive of an amortization schedule?

Accepted Answer

An amortization schedule typically involves payments that are the same total amount each period, but the portion of each payment that goes towards interest decreases over time, while the portion that goes towards the principal increases. This means that the same dollar amount of interest is not paid with each payment; instead, the interest portion decreases with each payment.

Question 5

Jill Clinton puts $1,000 in a savings passbook that pays 4% compounded quarterly. How much will she have in her account after five years?

Accepted Answer

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the amount after t years
P = the principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = the number of years

In this case: 
P = $1,000
r = 4% or 0.04
n = 4 (since interest is compounded quarterly)
t = 5

Plugging in the values, we get: 
A = $1,000(1 + 0.04/4)^(4*5)
A ≈ $1,220.20

Therefore, Jill will have $1,220.20 in her account after five years. The correct answer is B.

Question 6

Christine has just purchased a used Mercedes for $18,995. She plans to make a $2,500 down payment on the new car. What is the amount of her monthly payment on the remaining loan if she must pay 12% annual interest on a 24-month car loan?

Accepted Answer

First, we need to calculate the amount of the loan. Since Christine made a $2,500 down payment, the amount of the loan is:

Loan amount = purchase price - down payment
Loan amount = $18,995 - $2,500
Loan amount = $16,495

Next, we need to calculate the monthly payment on the loan. We can use the following formula to calculate the monthly payment:

P = (r * A) / (1 - (1 + r)^(-n))

Where:
P = monthly payment
r = monthly interest rate (annual interest rate divided by 12)
A = loan amount
n = total number of payments (number of years times 12)

In this case, r = 0.12/12 = 0.01, A = $16,495, and n = 24. Plugging in these values, we get:

P = (0.01 * $16,495) / (1 - (1 + 0.01)^(-24))
P = $776.48

Therefore, the amount of Christine's monthly payment on the loan is $776.48. The best choice is B.

Question 7

Assume a lender offers you a $25,000, 10%, three-year loan that is to be fully amortized with three annual payments. The first payment will be due one year from the loan date. How much will you have to pay each year?

Accepted Answer

The annual payment can be calculated using the formula for an amortizing loan: Payment = [P * r * (1 + r)^n] / [(1 + r)^n – 1], where P is the principal ($25,000), r is the annual interest rate (10% or 0.10), and n is the number of payments (3). This calculation results in an annual payment of approximately $10,053.

Question 8

Moe borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments. The interest paid in the first year is

Accepted Answer

The interest paid in the first year is calculated by applying the annual interest rate to the initial loan amount. Therefore, the interest for the first year is 11% of $10,500, which is $1,155.

Question 9

You borrow $10,000 to pay for your college tuition. The loan is amortized over a three-year period with an interest rate of 18%. What is your remaining balance at the end of Year Two?

Accepted Answer

In order to find the remaining balance at the end of Year Two, we need to calculate the payments made up to that point. The loan is amortized over a three-year period, so there will be 36 monthly payments. We can use a loan amortization calculator or formula to find the monthly payment, which is $361.35.

After making 24 payments (2 years x 12 months), we will have paid a total of $8,672.36 ($361.35 x 24). However, this amount includes both principal and interest, so we need to subtract the amount of principal paid during the first two years.

Using an amortization table or formula, we can find that the total amount of principal paid during the first two years is $6,774.43. Subtracting this amount from the total payments made gives us a remaining balance of $1,897.93. This means that the answer is C, $3,898, which is the closest option to our calculated remaining balance.

Question 10

The rate of interest actually paid or earned, also called the annual percentage rate (APR), is the ________ interest rate.

Accepted Answer

The annual percentage rate (APR) is the stated interest rate, which does not account for compounding within the year.

Question 11

Tom Vu deposited $5,000 in a savings account that paid 8% interest compounded quarterly. What is the effective rate of interest?

Accepted Answer

To find the effective rate of interest, we use the formula:
Effective rate = (1 + (nominal rate / n))^n - 1
Where, nominal rate = 8%
n = number of compounding periods per year = 4 (quarterly)
Plugging in the values, we get:
Effective rate = (1 + (0.08 / 4))^4 - 1
= 1.0824 - 1
= 0.0824 or 8.24% (rounded to two decimal places)
Therefore, the correct answer is B.

Question 12

If the quarterly rate of interest is 2.5% and interest is compounded quarterly, then the APR is:

Accepted Answer

The answer of If the quarterly rate of interest is...

Question 13

If the quarterly rate of interest is 2.5% and interest is compounded quarterly, then the EAR is:

Accepted Answer

To calculate EAR (Effective Annual Rate) we use the formula:
EAR = (1 + r/n)^n - 1, where r is the quarterly rate of interest and n is the number of times interest is compounded in a year.

So, for this question, we have:
r = 2.5%
n = 4 (since interest is compounded quarterly)

Plugging these values into the formula, we get:
EAR = (1 + 0.025/4)^4 - 1
EAR = 0.1038 or 10.38%

Therefore, the answer is A) 10.38%.

Question 14

The interest rate that measures the true interest rate when compounding occurs more frequently than once a year is called the:

Accepted Answer

The effective annual rate (EAR) takes compounding into account, allowing for an accurate representation of the true cost of borrowing or the true return on investment. The APR, compound rate of interest, and stated rate of interest do not reflect the impact of compounding.

Question 15

The interest rate determined by multiplying the interest rate charged per period by the number of periods in a year is called the:

Accepted Answer

The annual percentage rate (APR) is the interest rate for a whole year (annualized), rather than just a monthly fee/rate, as applied on a loan, mortgage loan, credit card, etc. It is a finance charge expressed as an annual rate.

Question 16

The time value concept/calculation used in amortizing a loan is

Accepted Answer

Amortizing a loan involves calculating the equal periodic payments required to fully repay the loan, including interest, over a specified time period. This requires the use of the present value of an annuity concept, which calculates the value of a series of equal periodic payments discounted back to their present value. The interest rate used in the present value calculation is typically the rate at which the loan was issued.

Question 17

A loan that is repaid in equal payments over a specified time period is called a (n)

Accepted Answer

An amortized loan is a loan that requires equal payments over a specified time period, with each payment consisting of a portion of the loan principal and interest. This ensures that the loan is fully paid off by the end of the specified time period. A discount loan involves the borrower receiving less than the face value of the loan upfront, and repaying the full value at a later date. A balloon loan involves making low payments for a period of time, with a large payment (the "balloon payment") due at the end. Therefore, the best choice is C.

Question 18

The method of calculating interest on a loan that is set by law is called the:

Accepted Answer

The annual percentage rate (APR) is the method of calculating interest on a loan that is set by law. It includes not only the interest rate but also any additional fees or charges associated with the loan, providing a standardized way for borrowers to compare the costs of different loan options. The negotiated legal rate (NLR) refers to the interest rate that lenders and borrowers agree upon through negotiation, and the effective annual rate (EAR) is a calculation of the total cost of borrowing over the course of a year, taking compounding into account.

Question 19

When compounding more than once a year, the true opportunity costs measure of the interest rate is indicated by the:

Accepted Answer

When compounding more than once a year, the effective annual rate (EAR) is the true measure of the interest rate, as it takes into account the compounding effect. The annual percentage rate (APR), contract rate, and stated rate only reflect the nominal interest rate without considering compounding. Therefore, the effective annual rate (EAR) is the best choice for indicating the true opportunity cost of interest rate when compounding occurs more than once a year.

Question 20

Consolidated Freightways is financing a new truck with a loan of $60,000 to be repaid in six annual end-of-year installments of $13,375. What annual interest rate is Consolidated Freightways paying?

Accepted Answer

The loan is an annuity problem where the present value of the annuity (loan amount) is $60,000, and the annuity payment is $13,375 for six years. Using the formula for the present value of an annuity, the interest rate that equates these values is approximately 9%.

Quiz 9: Time Value of Money