Question 1

Suppose you put $100 into a savings account today, the account pays 8% compounded semiannually, and you withdraw $50 one year after your initial deposit. What would your ending balance be 20 years after the initial $100 deposit was made, assuming that you make no additional deposits?

Accepted Answer

First we need to find the balance after one year, when $50 is withdrawn. Using the formula for compound interest compounded semiannually:

$A=P\left(1+\frac{r}{n}\right)^{nt}=100\left(1+\frac{0.08}{2}\right)^{2}-50\approx\boxed{129.16}$

Now we need to find the balance 20 years later using the same formula:

$A=129.16\left(1+\frac{0.08}{2}\right)^{2\cdot20}\approx\boxed{258.16}$
which is (C).

Question 2

Find the future value in two years of $100 that is deposited in an account, which pays 12%, compounded monthly.

Accepted Answer

We can use the formula $FV=P(1+r/n)^{nt}$, where P is the principal (100), r is the annual interest rate (12%), n is the number of times the interest is compounded per year (12), and t is the time in years (2). Plugging in these values, we get $FV=100(1+0.12/12)^{12*2}=126.97$. Therefore, the correct answer is E.

Question 3

You deposited $2,000 seven years ago and haven't touched the account since. Now you have $3,656 in the bank. What was the interest rate?

Accepted Answer

The answer of You deposited $2,000 seven years ago and...

Question 4

Comet Powder Company has purchased a piece of equipment costing $100,000. It is expected to generate a 10-year stream of benefits amounting to $16,273 per year. Determine the rate of return Comet expects to earn from this equipment.

Accepted Answer

To determine the rate of return, we need to use the formula: 
Rate of return = (Total benefits - Cost of equipment) / Cost of equipment

Plugging in the numbers: 
Rate of return = ($16,273 x 10 - $100,000) / $100,000 
Rate of return = $62,730 / $100,000 
Rate of return = 0.6273 or 62.73%

However, we need to keep in mind that the question asks for the rate of return expected by Comet, not the actual rate of return. Therefore, we can assume that Comet expects to earn a rate of return equal to the discount rate they use in their calculations. Since the benefits are spread over 10 years, we can assume that the discount rate is also the annual rate of return.

So, the expected rate of return would be the discount rate used by Comet, which we do not have access to. The closest answer choice is 10%, so the best choice is C.

Question 5

Your local bank offers 4-year certificates of deposit (CDs)12 % compounded quarterly. How much additional interest will you earn over 4 years on a $10,000 CD that is compounded quarterly, compared with one that is compounded annually?

Accepted Answer

First, we need to calculate how much interest the CD will earn when compounded quarterly:

- Quarterly interest rate: 12% / 4 = 3%
- Number of compounding periods: 4 years x 4 quarters per year = 16 quarters
- Final balance: $10,000 x (1 + 0.03)^16 = $14,802.46

Now, we need to calculate how much interest the CD will earn when compounded annually:

- Annual interest rate: 12%
- Number of compounding periods: 4 years x 1 = 4 years
- Final balance: $10,000 x (1 + 0.12)^4 = $14,802.28

The difference between the two balances is:

$14,802.46 - $14,802.28 = $0.18

Therefore, the additional interest earned when the CD is compounded quarterly compared to annually is $0.18, which is closest to option C) $312. This answer is incorrect, so the correct answer is B) $0.

Question 6

If an 8-year annuity due has a Future Value (FV)of $10,000 and the interest rate is 7%, what is the amount of each annuity payment?

Accepted Answer

The answer of If an 8-year annuity due has a...

Question 7

What is the rate of interest on a $10,000 loan that is to be repaid in 10 equal annual installments of $1,917.

Accepted Answer

The formula to calculate the interest rate on an installment loan is:
Interest Rate = (Installment Amount x Total Number of Installments - Loan Amount) / (Loan Amount x Total Number of Installments) x 100%
Plugging in the given values:
Interest Rate = (1917 x 10 - 10000) / (10000 x 10) x 100% 
Interest Rate = 14%
Therefore, the answer is (C) 14%.

Question 8

How much will you have at the end of 5 years in a European vacation account if you deposit $200 a month, and the account earns 12 percent compounded monthly?

Accepted Answer

The answer of How much will you have at the...

Question 9

You wish to save $500,000 in the next 25 years. You notice that a corporate bond fund that earns about 11 percent per year and decide to invest in it. How much must you save each year to obtain your goal?

Accepted Answer

To find the annual savings required, use the future value of an annuity formula: FV = Pmt * [(1 + r)^n - 1] / r. Here, FV = $500,000, r = 0.11, and n = 25. Solving for Pmt gives approximately $4,370.13.

Question 10

What is the amount of the equal annual installments for a 10-year, $10,000 loan with a 20% rate of interest?

Accepted Answer

The equal annual installment can be calculated using the formula:
Annual installment = Loan amount / Annuity factor
where annuity factor can be calculated using the formula:
Annuity factor = (1 - (1+i)^(-n)) / i
where i is the rate of interest and n is the number of years.
Plugging in the values, we get:
Annuity factor = (1 - (1+0.2)^(-10)) / 0.2 = 5.054
Annual installment = 10,000 / 5.054 = $1,978.68 or approximately $2,385.
Therefore, the correct answer is C.

Question 11

Your brother, who is 6 years old, just received a trust fund that will be worth $25,000 when he is 21 years old. If the fund earns 10 percent interest compounded annually, what is the value of the fund today?

Accepted Answer

We can use the formula for compounding interest, which is A = P(1+r/n)^(nt), where A is the ending amount, P is the beginning principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the values, we have P = 0 (since we want to find the present value), A = 25,000, r = 0.10, n = 1, and t = 15 (since the brother is currently 6 years old and the money will be received at 21).

So, A = P(1+r/n)^(nt) becomes 25,000 = P(1+0.10/1)^(1*15), which simplifies to 25,000 = P(2.594).

Solving for P, we get P = 25,000/2.594, which is approximately $9,652. Therefore, the value of the fund today is approximately $9,652. The closest answer choice to this is C, $5,975.

Question 12

If you deposit $3500 in a bank account paying 6% interest and leave it there for fifteen years, how much will you have?

Accepted Answer

Using the formula for compound interest: A = P(1 + r/n)^(nt), 
where A is the amount of money accumulated after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the number of years. 
Plugging in the given values, we get: 
A = 3500(1 + 0.06/1)^(1*15) = $8388.10
Therefore, the best choice is C.

Question 13

The Summer Breeze Hotel borrowed $100,000 from the Meadowlands Bank to pay for a new air conditioning system. The loan is for a period of 5 years at an interest rate of 10% and requires 5 equal end-of-year payments that include both principal and interest on the outstanding balance. What will be the outstanding balance after the third payment?

Accepted Answer

The answer of The Summer Breeze Hotel borrowed $100,000 from...

Question 14

What amount received at the end of 15 years is equivalent to $100 received at the end of each year for 15 years if the interest rate is 12%?

Accepted Answer

The future value of an annuity is given by the formula:FV = PMT * [(1 + r)^n - 1] / rwhere:PMT is the payment amountr is the interest raten is the number of periodsIn this case, PMT = $100, r = 12%, and n = 15. Plugging these values into the formula, we get:FV = $100 * [(1 + 0.12)^15 - 1] / 0.12= $100 * [3.728 - 1] / 0.12= $100 * 2.728 / 0.12= $3,728Therefore, the amount received at the end of 15 years is equivalent to $3,728 received at the end of each year for 15 years if the interest rate is 12%.

Question 15

Jane wants to have $200,000 in an account in 20 years. If it earns 11 percent per annum over the accumulation period, how much must she save per year (end of year)to have the $200,000?

Accepted Answer

The answer of Jane wants to have $200,000 in an...

Question 16

You know you will need $25,000 at the end of 5 years. How much would you have to deposit annually, starting at the end of the first year, into an account earning 10% to accumulate the needed amount?

Accepted Answer

The formula to calculate the annual deposit needed to accumulate a certain amount at a certain interest rate over a certain number of years is:
Annual deposit = (Future value / Present value factor) x (interest rate / Present value factor for annuity)
Present value factor = (1 + interest rate)^(-number of years)
Present value factor for annuity = [(1 + interest rate)^(-number of years) - 1] / interest rate
Plugging in the given values, we get:
Annual deposit = (25,000 / 0.6209) x (0.10 / 3.7908) = $4,095. Therefore, the best choice is (B).

Question 17

An annuity with $1,000 annual payments at the end of each year, with a 10% interest rate, is worth how much at the end of four years?

Accepted Answer

The future value of an annuity is calculated using the formula: FV = P * [(1 + r)^n - 1] / rwhere:P is the annual paymentr is the interest raten is the number of yearsIn this case, P = $1,000, r = 10%, and n = 4. Plugging these values into the formula, we get:FV = $1,000 * [(1 + 0.10)^4 - 1] / 0.10= $1,000 * [1.4641 - 1] / 0.10= $1,000 * 0.4641= $4,641.00Therefore, the annuity is worth $4,641.00 at the end of four years.

Question 18

Joan is saving to open her own dress shop in 10 years. She currently has $10,000. In addition, she plans to save $2,000 per year for the next 5 years and $3,000 per year for the following 5 years. How much will Joan have in 10 years if she earns a 10 % return on her savings?

Accepted Answer

In 5 years, Joan will save:
$2,000/year x 5 years = $10,000
In the following 5 years, Joan will save:
$3,000/year x 5 years = $15,000
After 10 years, Joan will have:
Initial investment: $10,000
Plus savings over 10 years: $10,000 + $10,000 + $15,000 = $35,000
Plus interest earned on investments: $35,000 x 1.10^10 = $63,925.12
Therefore, Joan will have $63,925 in 10 years with a 10% return on her savings.

Question 19

Calculate the amount today that is equivalent to $150 at the end of year 1, $450 at the end of year 2, and $300 at the end of year 3, given a discount rate of 10%.

Accepted Answer

We need to calculate the present value of each amount and then sum them up. Using the formula to calculate the present value of a future amount:
PV = FV / (1 + r)^n
where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.

PV(Y1) = $150 / (1 + 0.1)^1 = $136.36
PV(Y2) = $450 / (1 + 0.1)^2 = $330.58
PV(Y3) = $300 / (1 + 0.1)^3 = $220.47

Therefore, the total present value is:
PV(total) = $136.36 + $330.58 + $220.47 = $687.41

The closest answer choice to this amount is D) $734, which is the best choice.

Question 20

Which of the following cash flows has the highest present value (PV)at a 15 percent discount rate?

Accepted Answer

The present value of $300 received every year for 5 years at a 15% discount rate is higher than the other options when calculated using the present value of an annuity formula.

Quiz 6: Time Value of Money