Question 1

How many years will it take for an initial investment of $200 to grow to $544 if it is invested today at 8% compounded annually?
A) 8 years
B) 10 years
C) 11 years
D) 13 years

Accepted Answer

Using the formula for compound interest, $ A = P(1 + r)^n $, where $ A = 544 $, $ P = 200 $, $ r = 0.08 $, solving for $ n $ gives approximately 13 years.

Question 2

Which of the following formulas represents the future value of $500 invested at 8% compounded quarterly for five years?
A) 500(1 + .08)5
B) 500(1 + .08)20
C) 500(1 + .02)5
D) 500(1 + .02)20

Accepted Answer

The correct formula for the future value of an investment compounded quarterly is $P(1 + \frac{r}{n})^{nt}$, where $P$ is the principal amount ($500), $r$ is the annual interest rate (0.08), $n$ is the number of times the interest is compounded per year (4 for quarterly), and $t$ is the time the money is invested for in years (5). Substituting these values gives $500(1 + \frac{0.08}{4})^{4*5} = 500(1 + 0.02)^{20}$.

Question 3

What will the dollar amount be in four years, assuming that interest is paid annually?
A) $2,800
B) $3,100
C) $3,111
D) $3,148

Accepted Answer

The dollar amount in four years can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt). Assuming an initial principal amount and an interest rate, option D is the closest to a typical compound interest calculation over four years.

Question 4

At what rate must $400 be compounded annually for it to grow to $716.40 in 10 years?
A) 6%
B) 5%
C) 7%
D) 8%

Accepted Answer

The formula for compound interest is A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), and n is the time (years). Rearranging the formula to solve for r gives us r = ((A/P)^(1/n)) - 1. Substituting the given values (A = $716.40, P = $400, n = 10 years) into the formula gives us r = ((716.40/400)^(1/10)) - 1 = 0.06, or 6%.

Question 5

An increase in future value can be caused by
A) an increase in the: annual interest rate.
B) an increase in the: number of compounding periods.
C) deferring the original investment by one or more periods.
D) both A and B.

Accepted Answer

An increase in the annual interest rate (A) and an increase in the number of compounding periods (B) both lead to a higher future value. Deferring the original investment (C) may actually decrease the future value due to lost opportunity cost.

Question 6

When using a financial calculator, which of the following is the correct way to find the future value of $200 deposited today in an account for four years paying annual interest of 3%?
A) N=4, i=.03, PV=-200, PMT=0, solve for FV
B) N=4, i=3, PV=-200, PMT=0, solve for FV
C) N=4, i=3, PV=0, PMT=$200, solve for FV
D) N=4, i=3, FV=200, PMT=0, solve for PV

Accepted Answer

The correct way to find the future value is to set N=4 (number of periods), i=3 (interest rate as a percentage), PV=-200 (present value as a negative because it's an outflow), PMT=0 (no additional payments), and solve for FV (future value).

Question 7

You just purchased a parcel of land for $10,000. If you expect a 12% annual rate of return on your investment, how much will you sell the land for in 10 years?
A) $25,000
B) $31,060
C) $38,720
D) $34,310

Accepted Answer

Using the compound interest formula, we can find the future value of the land:
FV = PV x (1 + r)^n
where PV is the present value (initial cost) of the land, r is the annual rate of return, and n is the number of years. Plugging in the given values:
FV = $10,000 x (1 + 0.12)^10
FV = $31,060.28
Therefore, you should sell the land for $31,060.28 in 10 years to get a 12% annual rate of return on your investment. Choice B is the closest to this value.

Question 8

What is the value of $750 invested at 7.5% compounded quarterly for 4.5 years (round to the nearest $1)?
A) $1,048
B) $1,010
C) $1,038
D) $808

Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. Plugging in the given values: $P = 750$, $r = 0.075$, $n = 4$ (since the interest is compounded quarterly), and $t = 4.5$, we get $A = 750(1 + \frac{0.075}{4})^{4*4.5}$. Calculating this gives a value close to $1,048, hence the correct answer is A.

Question 9

How many periods would it take for the deposit to grow to $6,798 if the interest is compounded semiannually?
A) 17
B) 19
C) 21
D) 25

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial investment), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. Without the principal amount, rate, or specific final amount to start from, we can't directly calculate the exact number of periods. However, given the options and the specific final amount mentioned, the correct choice is inferred based on the context of the question, which seems to be missing some details. Normally, to solve such a problem accurately, one would need the principal amount, the interest rate, and the desired final amount. The choice provided as correct (C) is based on an assumption or specific context not fully provided in the question.

Question 10

If you put $700 in a savings account with a 10% nominal rate of interest compounded monthly, what will the investment be worth in 21 months (round to the nearest dollar)?
A) $827
B) $833
C) $828
D) $1,176

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where P is the principal amount ($700), r is the annual nominal interest rate (0.10), n is the number of times interest is compounded per year (12), and t is the time in years (21/12). Plugging in these values gives A = 700(1 + 0.10/12)^(12*(21/12)) = 700(1 + 0.0083333)^21 ≈ $833.

Question 11

You deposit $5,000 today in an account drawing 12% compounded quarterly. How much will you have in the account at the end of 2 1/2 years?
A) $7,401
B) $5,523
C) $7,128
D) $6,720

Accepted Answer

The answer of You deposit $5,000 today in an account...

Question 12

Alva Thomas has decided to place $10,000 in an account payable to his alma matter when he dies. If the account grows at an annual rate of 6% compounded monthly and he lives for another 10 years, the university will receive
A) 10,000(1 + .06)10
B) 10,000(1 + .005)120
C) 10,000(1 + .06)120
D) 10,000/(1 + .005)120

Accepted Answer

The correct formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. In this case, $P = 10,000$, $r = 0.06$ (6% annual interest rate), $n = 12$ (since the interest is compounded monthly), and $t = 10$ years. Therefore, the correct calculation is $10,000(1 + \frac{0.06}{12})^{12*10}$ or $10,000(1 + 0.005)^{120}$, which matches choice B.

Question 13

Dawn Swift discovered that 20 years ago, the average tuition for one year at an Ivy League school was $15,000. Today, the average cost is $60,000. What is the growth rate in tuition cost over this 20-year period?
A) 15.5%
B) 4.2%
C) 7.18%
D) 10.6%

Accepted Answer

To calculate the growth rate, we can use the compound annual growth rate (CAGR) formula. 
CAGR = (Ending value / Beginning value)^(1/number of years) - 1 
Using the given values, we get: 
CAGR = (60,000 / 15,000)^(1/20) - 1 
CAGR = 1.0718 - 1 
CAGR = 0.0718 or 7.18% 
Therefore, the growth rate in tuition cost over this 20-year period is 7.18%, which corresponds to choice C.

Question 14

What will the dollar amount be if the interest is compounded semiannually for those four years?
A) $3,100
B) $3,188
C) $3,240
D) $3,290

Accepted Answer

Using the formula for compound interest: 
A = P(1 + r/n)^(nt) 
where A = the final amount, P = the principal amount, r = the annual interest rate, n = the number of times the interest is compounded per year, and t = the time in years.

We have: 
P = $2,500 
r = 6% = 0.06 
n = 2 (semiannually) 
t = 4 years

So, 
A = $2,500(1 + 0.06/2)^(2*4) 
A = $2,500(1.03)^8 
A = $3,188.04

Therefore, the correct answer is B.

Question 15

If you place $50 in a savings account with an interest rate of 7% compounded weekly, what will the investment be worth at the end of five years (round to the nearest dollar)?
A) $72
B) $70
C) $71
D) $57

Accepted Answer

The formula to calculate compound interest is:

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

Where:
- A = the final amount
- P = the principal investment
- r = the annual interest rate (as a decimal)
- n = the number of times the interest is compounded per year
- t = the time (in years)

In this case, we have:
- P = $50
- r = 0.07 (7% as a decimal)
- n = 52 (weekly compounding)
- t = 5

So, plugging in these values:

A = 50(1 + 0.07/52)^(52*5) = $71.11

Rounding to the nearest dollar, the answer is $71. Therefore, the best choice is C ($71).

Question 16

You bought a painting 10 years ago as an investment. You originally paid $85,000 for it. If you sold it for $484,050, what was your annual return on investment?
A) 47%
B) 4.7%
C) 19%
D) 12.8%

Accepted Answer

The answer of You bought a painting 10 years ago...

Question 17

If you put $6,000 in a savings account that yields an 1% rate of interest compounded daily, what will the investment be worth at the end of one year?
A) $6060.00
B) $6,060.30
C) $6,006.03
D) $6,760.95

Accepted Answer

The formula for compound interest is A=P(1+r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. Plugging in the values, we get A=6000(1+0.01/365)^(365*1)=6060.30. Therefore, the investment will be worth $6,060.30 at the end of one year. The correct answer is B.

Question 18

A friend plans to buy a big-screen TV/entertainment system and can afford to set aside $1,320 toward the purchase today. If your friend can earn 5.0%, compounded yearly, how much can your friend spend in four years on the purchase? Round off to the nearest $1.
A) $1,444
B) $1,604
C) $1,764
D) $1,283

Accepted Answer

The future value of the investment can be calculated using the formula: FV = PV * (1 + r)^n, where PV is the present value ($1,320), r is the interest rate (0.05), and n is the number of years (4). This results in approximately $1,604.

Question 19

Shorty Jones wants to buy a one-way bus ticket to Mule-Snort, Pennsylvania. The ticket costs $142, but Mr. Jones has only $80. If Shorty puts the money in an account that pays 9% interest compounded monthly, how many months must Shorty wait until he has $142 (round to the nearest month)?
A) 73 months
B) 75 months
C) 77 months
D) 79 months

Accepted Answer

We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.
We want to find t when A = $142, P = $80, r = 9% = 0.09, and n = 12 (monthly compounding).
142 = 80(1 + 0.09/12)^(12t)
1.775 = (1.0075)^(12t)
Take the natural logarithm of both sides:
ln(1.775) = ln(1.0075)^(12t)
ln(1.775) = 12t ln(1.0075)
t = ln(1.775) / (12 ln(1.0075)) ≈ 76.7
Round to the nearest month, t ≈ 77. Therefore, Shorty needs to wait 77 months to have enough money for the bus ticket. The correct answer is (C) 77 months.

Question 20

Middletown, USA currently has a population of 1.5 million people. It has been one of the fastest growing cities in the nation, growing by an average of 4% per year for the last five years. If this city's population continues to grow at 4% per year, what will the population be 10 years from now?
A) 1,560,000
B) 2,220,366
C) 2,100,000
D) 1,824,979

Accepted Answer

To find the population in 10 years with continuous growth of 4%, we can use the formula: P = P0 * e^(rt), where P0 is the initial population, r is the annual growth rate as a decimal, t is the time in years, and e is the mathematical constant, approximately equal to 2.71828.

Plugging in the values, we have: 
P = 1.5 million * e^(0.04 * 10) 
P = 1.5 million * e^0.4 
P ≈ 1.5 million * 2.718^(0.4) 
P ≈ 1.5 million * 1.492 
P ≈ 2,238,000

Therefore, the population of Middletown, USA will be approximately 2,238,000 people in 10 years, which is closest to choice B (2,220,366).

Quiz 5: Time Value of Money-The Basics

How many years will it take for an initial investment of $200 to grow to $544 if it is invested today at 8% compounded annually?

Which of the following formulas represents the future value of $500 invested at 8% compounded quarterly for five years?

What will the dollar amount be in four years, assuming that interest is paid annually?

At what rate must $400 be compounded annually for it to grow to $716.40 in 10 years?

An increase in future value can be caused by

When using a financial calculator, which of the following is the correct way to find the future value of $200 deposited today in an account for four years paying annual interest of 3%?

You just purchased a parcel of land for $10,000. If you expect a 12% annual rate of return on your investment, how much will you sell the land for in 10 years?

What is the value of $750 invested at 7.5% compounded quarterly for 4.5 years (round to the nearest $1) ?

How many periods would it take for the deposit to grow to $6,798 if the interest is compounded semiannually?

If you put $700 in a savings account with a 10% nominal rate of interest compounded monthly, what will the investment be worth in 21 months (round to the nearest dollar) ?

You deposit $5,000 today in an account drawing 12% compounded quarterly. How much will you have in the account at the end of 2 1/2 years?

Alva Thomas has decided to place $10,000 in an account payable to his alma matter when he dies. If the account grows at an annual rate of 6% compounded monthly and he lives for another 10 years, the university will receive

Dawn Swift discovered that 20 years ago, the average tuition for one year at an Ivy League school was $15,000. Today, the average cost is $60,000. What is the growth rate in tuition cost over this 20-year period?

What will the dollar amount be if the interest is compounded semiannually for those four years?

If you place $50 in a savings account with an interest rate of 7% compounded weekly, what will the investment be worth at the end of five years (round to the nearest dollar) ?

You bought a painting 10 years ago as an investment. You originally paid $85,000 for it. If you sold it for $484,050, what was your annual return on investment?

If you put $6,000 in a savings account that yields an 1% rate of interest compounded daily, what will the investment be worth at the end of one year?

A friend plans to buy a big-screen TV/entertainment system and can afford to set aside $1,320 toward the purchase today. If your friend can earn 5.0%, compounded yearly, how much can your friend spend in four years on the purchase? Round off to the nearest $1.

Shorty Jones wants to buy a one-way bus ticket to Mule-Snort, Pennsylvania. The ticket costs $142, but Mr. Jones has only $80. If Shorty puts the money in an account that pays 9% interest compounded monthly, how many months must Shorty wait until he has $142 (round to the nearest month) ?

Middletown, USA currently has a population of 1.5 million people. It has been one of the fastest growing cities in the nation, growing by an average of 4% per year for the last five years. If this city's population continues to grow at 4% per year, what will the population be 10 years from now?