Question 1

Annette has a loan that requires a $25,000 payment at the end of three years.The interest rate on the loan is 5%, compounded annually.How much did Annette borrow today?

Accepted Answer

Present Value = Future Value * Interest Factor
Present Value = $25,000 * 0.8638 = $21,595
0.8638 is the interest factor on the Present Value table; n = 3; i = 5%

Question 2

What is interest?

Accepted Answer

The answer of What is interest?...

Question 3

Explain the concept of the present value of a single amount.

Accepted Answer

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Question 4

What amount can you borrow if you make six quarterly payments of $4,000 at a 12 % annual rate of interest?

Accepted Answer

Using the formula for the future value of an annuity due, where:
- P = payment amount = $4,000
- r = interest rate per period = 12%/4 = 3%
- n = total number of periods = 6
- FVAD = future value of the annuity due
FVAD = P[(1+r)^n - 1]/r * (1+r)
FVAD = $4,000[(1+0.03)^6 - 1]/0.03 * 1.03
FVAD = $28,999.20
Therefore, the maximum amount that can be borrowed is $21,668.80 (rounded to the nearest cent) since this is the present value of the annuity due at an annual interest rate of 12% for six quarters:
PV = FVAD/(1+r)^6
PV = $28,999.20/(1+0.12/4)^6
PV = $21,668.80 (rounded to the nearest cent)

Question 5

Jon Shear expects an investment of $25,000 to return $6,595 annually.His investment is earning 10% per year.How many annual payments will he receive?

Accepted Answer

Present Value of an Annuity = Annuity * Interest Factor
$25,000 = $6,595 * Interest Factor; Interest Factor = 0.3.7908
3.7908 is the interest factor on the Present Value of an Annuity table; i = 10%; n = 5

Question 6

How long will it take an investment of $25,000 at 6% compounded annually to accumulate to a total of $35,462.50?

Accepted Answer

We can use the formula for compound interest:

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

Where A is the final amount, P is the principal (starting amount), r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we have:

P = $25,000
r = 6% = 0.06
n = 1 (compounded annually)
A = $35,462.50

Plugging these values into the formula, we get:

$35,462.50 = $25,000*(1+0.06/1)^(1*t)

Dividing both sides by $25,000 and simplifying, we get:

1.4185 = 1.06^t

Taking the natural logarithm of both sides, we get:

ln(1.4185) = t*ln(1.06)

Solving for t, we get:

t = ln(1.4185)/ln(1.06) ≈ 6.05

So, it will take about 6 years (rounded to the nearest year) for the investment to accumulate to $35,462.50. The best choice is C) 6 years.

Question 7

Chad is setting up a retirement fund, and he plans on depositing $5,000 per year in an investment that will pay 7% annual interest.How long will it take him to reach his retirement goal of $69,080?

Accepted Answer

Future Value of an Annuity = Annuity * Interest Factor
$69,080 = $5,000 * Interest Factor; Interest Factor = 13.816
13.816 is the interest factor on the Future Value of an Annuity table; i= 7%; n = 10
Short Essay Questions

Question 8

A company is creating a fund by depositing $65,763 today.The fund will grow to $90,000 after eight years.What annual interest rate is the company earning on the fund?

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Question 9

A company is considering an investment that will return $20,000 at the end of each semiannual period for four years.If the company requires an annual return of 10%, what is the maximum amount it is willing to pay for this investment?

Accepted Answer

The answer of A company is considering an investment that...

Question 10

Explain the concept of the present value of an annuity.

Accepted Answer

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Question 11

A company expects to invest $5,000 today at 12% annual interest and plans to receive $15,529 at the end of the investment period.How many years will elapse before the company accumulates the $15,529?

Accepted Answer

The answer of A company expects to invest $5,000 today...

Question 12

Crowe Company has acquired a building with a loan that requires payments of $20,000 every six months for five years.The annual interest rate on the loan is 12%.What is the present value of the building?

Accepted Answer

We can use the present value formula for an annuity to calculate the present value of the loan payments.

PV = PMT x (1 - (1 + r/n)^-nt) / (r/n)

Where PV is the present value, PMT is the payment amount, r is the annual interest rate, n is the number of times per year the payment is made, and t is the number of years.

Substituting the given values, we get:

PV = $20,000 x (1 - (1 + 0.12/2)^-2x5) / (0.12/2)
PV = $147,202

Therefore, the present value of the building is $147,202. Answer choice C is correct.

Question 13

Explain the concept of the future value of an annuity.

Accepted Answer

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Question 14

Sam has a loan that requires a single payment of $4,000 at the end of three years.The loan's interest rate is 6%, compounded semiannually.How much did Sam borrow?

Accepted Answer

$4,000 x 0.8375 = $3,350.00

Question 15

What interest rate is required to accumulate $6,802.50 in four years from an investment of $5,000?

Accepted Answer

Present Value = Future Value * Interest Factor
$5,000 = $6,802.50 * Interest Factor; Interest Factor = 0.7350
0.7350 is the interest factor on the Present Value table; n = 4; i = 8%
Or, Alternative Solution: Future Value = Present Value * Interest Factor
$6,802.50 = $5,000 * Interest Factor; Interest Factor = 1.3605
1.3605 is the interest factor on the Future Value table; n = 4; i = 8%

Question 16

Explain the concept of the future value of a single amount.

Accepted Answer

The answer of Explain the concept of the future value...

Question 17

Keisha has $3,500 now and plans on investing it in a fund that will pay her 12% interest compounded quarterly.How much will Keisha have accumulated after two years?

Accepted Answer

$3,500 x 1.2668 = $4,433.80

Question 18

An individual is planning to set-up an education fund for her children.She plans to invest $10,000 annually at the end of each year.She expects to withdraw money from the fund at the end of 10 years and expects to earn an annual return of 8%.What will be the total value of the fund at the end of 10 years?

Accepted Answer

Using the formula for future value of an annuity:
FV = Pmt x [(1 + r)^n - 1] / r
Where FV = future value, Pmt = annual deposit, r = rate of return, and n = number of years.

FV = $10,000 x [(1 + 0.08)^10 - 1] / 0.08
FV = $10,000 x 14.4867
FV = $144,867

Therefore, the total value of the fund at the end of 10 years will be $144,870. 
The best choice is D, because it is the only option that matches this calculation.

Question 19

Thompson Company has acquired a machine from a dealer which requires a payment of $45,000 at the end of five years.This transaction includes interest at 8%, compounded semiannually.What is the value of the machine today?

Accepted Answer

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Question 20

A company needs to have $200,000 in four years, and will create a fund to ensure that the $200,000 will be available.If they can earn a 7% return, how much must the company invest in the fund today to equal the $200,000 at the end of four years?

Accepted Answer

The answer of A company needs to have $200,000 in...

Quiz 14: Time Value of Money