Question 1

What principal earning 16% compounded quarterly will grow to $8,500 after six years and three months?
A) $448.66
B) $22,659.61
C) $3,188.49
D) $3,361.68
E) $3,147.71

Accepted Answer

C

Question 2

Calculate the present value of a payment of $27,500 payable in 10 years if money is worth 9% compounded semi-annually.
A) $29,723.88
B) $11,616.30
C) $11,402.68
D) $9,725.39
E) $8,899.11

Accepted Answer

The present value is calculated using the formula PV = FV / (1 + r/n)^(nt), where FV is the future value ($27,500), r is the annual interest rate (0.09), n is the number of compounding periods per year (2), and t is the number of years (10). Plugging in these values gives the present value as approximately $11,402.68.

Question 3

Laurel borrowed some money from Hardy 42 months ago. The loan principal plus interest at 17% compounded annually is to be repaid today. Laurel and Hardy agree that the total amount due is $31,618. How much did Laurel borrow from Hardy 42 months ago?
A) $10,618.49
B) $13,367.12
C) $18,250.88
D) $23,157.32
E) $49,868.89

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 (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 or borrowed for, in years. In this case, A = $31,618, r = 17% or 0.17, n = 1 (since the interest is compounded annually), and t = 42 months or 3.5 years. We need to solve for P. Rearranging the formula to solve for P gives us P = A / (1 + r/n)^(nt). Substituting the given values, we get P = $31,618 / (1 + 0.17/1)^(1*3.5) = $31,618 / (1.17)^3.5 ≈ $18,250.88.

Question 4

Calculate the maturity value of $18,559 after 7.5 years at 9% compounded quarterly.
A) $36,179
B) $31,086
C) $32,000
D) $53,776
E) $29,000

Accepted Answer

The correct answer is A because the maturity value of $18,559 after 7.5 years at 9% compounded quarterly is $36,179. This can be calculated using the formula:FV = PV * (1 + r/n)^(n*t)where:FV is the future valuePV is the present valuer is the annual interest raten is the number of times per year that the interest is compoundedt is the number of yearsIn this case, PV = $18,559, r = 9%, n = 4 (since the interest is compounded quarterly), and t = 7.5. Plugging these values into the formula, we get:FV = $18,559 * (1 + 0.09/4)^(4*7.5)= $18,559 * (1.0225)^30= $36,179

Question 5

Boris borrowed $500 five years ago. The interest rate on the loan was 9% compounded monthly for the first 27 months and 6% compounded quarterly for the rest of the time. How much does he owe now?
A) $878.27
B) $720.63
C) $846.92
D) $603.33
E) $751.90

Accepted Answer

The answer of Boris borrowed $500 five years ago. The...

Question 6

What amount was invested 35 years ago at 7% compounded semi-annually if the value of the investment has now grown to $1,000,000?
A) $634,757
B) $111,128
C) $103,549
D) $89,986
E) $57,637

Accepted Answer

The answer of What amount was invested 35 years ago...

Question 7

If you deposit $2,500 into an investment that grows at 13.2% compounded monthly, what will its value be in 17.5 years?
A) $24,870
B) $57,750
C) $21,890
D) $48,901
E) $16,211

Accepted Answer

The answer of If you deposit $2,500 into an investment...

Question 8

Money is worth 5% compounded semi-annually. What is the value today of a contract that will bring in a payment of $86,500 in nine years?
A) $63,276
B) $38,090
C) $55,461
D) $41,962
E) $55,759

Accepted Answer

The answer of Money is worth 5% compounded semi-annually. What...

Question 9

Helen's investment of $500 has grown, at a rate of 13% compounded annually, for 45 years. What is the maturity value of her investment?
A) $204,381
B) $129,667
C) $825
D) $82,592
E) $122,321

Accepted Answer

The answer of Helen's investment of $500 has grown, at...

Question 10

A nine-year, $270,000 promissory note bears interest at a rate of 8% compounded annually. What is its maturity value?
A) $$441,889
B) $$539,731
C) $299,057
D) $752,198
E) $135,067

Accepted Answer

The answer of A nine-year, $270,000 promissory note bears interest...

Question 11

What amount today is equivalent to $6,800 three years ago, if money earned 12% compounded quarterly over the past three years?
A) $8,872.46
B) $9,553.51
C) $9,695.17
D) $9,729.23
E) $4,769.38

Accepted Answer

To find the equivalent amount today of $6,800 from three years ago with an interest rate of 12% compounded quarterly, we use the formula for compound interest: $A = P(1 + \frac{r}{n})^{nt}$, 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.Given:- $P = $6,800$- $r = 12\% = 0.12$- $n = 4$ (since the interest is compounded quarterly)- $t = 3$ yearsPlugging these values into the formula gives us:$$A = 6800(1 + \frac{0.12}{4})^{4*3}$$$$A = 6800(1 + 0.03)^{12}$$$$A = 6800(1.03)^{12}$$$$A ≈ $9,695.17$$Therefore, the amount today equivalent to $6,800 three years ago, with the given interest conditions, is approximately $9,695.17.

Question 12

Betty borrowed $50 from Chuckie for 2 years at 9% compounded monthly. How much did she owe at the end of the two years?
A) $19.83
B) $59.82
C) $67.88
D) $54.16
E) $63.71

Accepted Answer

The answer of Betty borrowed $50 from Chuckie for 2...

Question 13

Everyone thought he was being foolish again when, 65 years ago, great-great-uncle Crazy Louie invested $150 in the common stock of a company that produced a carbonated soft drink in Atlanta Georgia. The value of the stock has grown at an average rate of 15% compounded semi-annually. What's the value of Crazy Louie's foolish investment now?
A) $13,559,733
B) $5,872,556
C) $1,816,317
D) $925,767
E) $146,250

Accepted Answer

The answer of Everyone thought he was being foolish again...

Question 14

Murphy's annual income has increased by 10% per year for the last 8 years. If Murphy's annual income is now $72,596, what was it 8 years ago?
A) $14,519
B) $33,867
C) $41,587
D) $51,922
E) $58,077

Accepted Answer

To find Murphy's income 8 years ago, we can use the formula for exponential decay, which in this context is the reverse of growth: $P = \frac{A}{(1 + r)^n}$, where $P$ is the principal amount (initial income), $A$ is the amount after $n$ years (final income), $r$ is the rate of increase, and $n$ is the number of years. Plugging in the values: $P = \frac{72,596}{(1 + 0.10)^8}$, which simplifies to approximately $33,867.

Question 15

Consider a graph of future values of two investments of $1000. How would you expect the graphs of the future values to look if both investment 1 earns 15% compounded annually, and investment 2 earns 10% compounded annually?
A) Investment 1 is steeper and the graph is growing at a faster rate.
B) Investment 2 is steeper and the graph is growing at a faster rate.
C) Investment 1 is steeper and the graph is growing at a slower rate.
D) Investment 2 is steeper and the graph is growing at a slower rate.
E) The two graphs look the same as they are both compounding interest.

Accepted Answer

Investment 1, with a higher interest rate of 15% compounded annually, will grow faster than Investment 2, which has a 10% annual compound rate, making its graph steeper.

Question 16

What is the maturity value of a $3,500 loan for 15 months at 12% compounded quarterly?
A) $3,019.13
B) $5,452.89
C) $4,063.39
D) $4,258.29
E) $4,057.46

Accepted Answer

The answer of What is the maturity value of a...

Question 17

If Smitty is able to earn 11% compounded semi-annually on his $750 investment, how much money will he have in 40 years?
A) $48,751
B) $54,357
C) $73,825
D) $89,324
E) $7,979

Accepted Answer

The answer of If Smitty is able to earn 11%...

Question 18

Consider a graph of future values of two investments of $1000. How would you expect the graphs of the future values to look if both investments earn 5% nominal rate, but investment 1 is compounded monthly and investment 2 is compounded semi-annually?
A) Investment 1 is steeper and the graph is growing at a faster rate.
B) Investment 2 is steeper and the graph is growing at a faster rate.
C) Investment 1 is steeper and the graph is growing at a slower rate.
D) Investment 2 is steeper and the graph is growing at a slower rate.
E) The two graphs look the same as they are both compounding interest.

Accepted Answer

The graph of Investment 1, which is compounded monthly, will grow at a faster rate than Investment 2, which is compounded semi-annually, due to the effects of more frequent compounding periods within a year.

Question 19

How much money would have to be invested today, at 9% compounded monthly in order to have $40,000 in seven years?
A) $21,353.81
B) $23,726.43
C) $33,786.03
D) $34,928.08
E) $5,071.92

Accepted Answer

To find the present value (the amount of money to be invested today) to achieve a future value of $40,000 in 7 years at a 9% annual interest rate compounded monthly, we use the formula for the present value of a single sum: $PV = \frac{FV}{(1 + r/n)^{nt}}$, where PV is the present value, FV is the future value ($40,000), r is the annual interest rate (0.09), n is the number of compounding periods per year (12), and t is the time in years (7). Plugging in the values, we get $PV = \frac{40,000}{(1 + 0.09/12)^{12*7}}$, which calculates to approximately $21,353.81.

Question 20

Twenty years ago Freddie invested $2,000. For the first 10 years he earned 13% compounded semi-annually. For the next 10 years he earned 8% compounded quarterly. What was the value of the investment now, at the end of the 20 years?
A) $5,927
B) $9,185
C) $17,292
D) $14,732
E) $15,561

Accepted Answer

First, calculate the value after the first 10 years with 13% semi-annual compounding: $ A = 2000 \times (1 + \frac{0.13}{2})^{20} $. Then, use this amount as the principal for the next 10 years with 8% quarterly compounding: $ A = A \times (1 + \frac{0.08}{4})^{40} $. The final amount is approximately $15,561.

Quiz 8: Compound Interest: Future Value and Present Value

What principal earning 16% compounded quarterly will grow to $8,500 after six years and three months?

Calculate the present value of a payment of $27,500 payable in 10 years if money is worth 9% compounded semi-annually.

Laurel borrowed some money from Hardy 42 months ago. The loan principal plus interest at 17% compounded annually is to be repaid today. Laurel and Hardy agree that the total amount due is $31,618. How much did Laurel borrow from Hardy 42 months ago?

Calculate the maturity value of $18,559 after 7.5 years at 9% compounded quarterly.

Boris borrowed $500 five years ago. The interest rate on the loan was 9% compounded monthly for the first 27 months and 6% compounded quarterly for the rest of the time. How much does he owe now?

What amount was invested 35 years ago at 7% compounded semi-annually if the value of the investment has now grown to $1,000,000?

If you deposit $2,500 into an investment that grows at 13.2% compounded monthly, what will its value be in 17.5 years?

Money is worth 5% compounded semi-annually. What is the value today of a contract that will bring in a payment of $86,500 in nine years?

Helen's investment of $500 has grown, at a rate of 13% compounded annually, for 45 years. What is the maturity value of her investment?

A nine-year, $270,000 promissory note bears interest at a rate of 8% compounded annually. What is its maturity value?

What amount today is equivalent to $6,800 three years ago, if money earned 12% compounded quarterly over the past three years?

Betty borrowed $50 from Chuckie for 2 years at 9% compounded monthly. How much did she owe at the end of the two years?

Murphy's annual income has increased by 10% per year for the last 8 years. If Murphy's annual income is now $72,596, what was it 8 years ago?

Consider a graph of future values of two investments of $1000. How would you expect the graphs of the future values to look if both investment 1 earns 15% compounded annually, and investment 2 earns 10% compounded annually?

What is the maturity value of a $3,500 loan for 15 months at 12% compounded quarterly?

If Smitty is able to earn 11% compounded semi-annually on his $750 investment, how much money will he have in 40 years?

Consider a graph of future values of two investments of $1000. How would you expect the graphs of the future values to look if both investments earn 5% nominal rate, but investment 1 is compounded monthly and investment 2 is compounded semi-annually?

How much money would have to be invested today, at 9% compounded monthly in order to have $40,000 in seven years?

Twenty years ago Freddie invested $2,000. For the first 10 years he earned 13% compounded semi-annually. For the next 10 years he earned 8% compounded quarterly. What was the value of the investment now, at the end of the 20 years?