Question 1

A 30-year, $1,000 strip bond was traded for $167, four years after it was issued. What was the semi-annually compounded nominal rate at that time?

Accepted Answer

B

Question 2

If the population of Green City is growing at a rate of 5% per year, how long will it take to grow from 2,300 to 10,000?

Accepted Answer

E

Question 3

Twenty years ago the population of a village in Newfoundland was 964. Now it is 612. At what average annual rate has the population of the village declined over the last 20 years?

Accepted Answer

C

Question 4

Albert Greco paid $1,974 for a $10,000 strip bond 16 years before it reached maturity. What semi-annually compounded nominal rate will Albert earn on his investment?

Accepted Answer

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Question 5

A demand loan for $8,000 with interest at 16% compounded quarterly was repaid after two years and eight months. What was the amount of interest paid?

Accepted Answer

The interest is calculated using the formula for compound interest: A = P(1 + r/n)^(nt). Here, P = $8,000, r = 0.16, n = 4, and t = 2 + 8/12 = 2.6667 years. The total amount A is calculated, and then the interest is A - P.

Question 6

If the population of Dodge City is decreasing at a rate of 19% per year, how long will it take to decrease from 7,700 to 2,000?

Accepted Answer

The population decrease can be modeled by the exponential decay formula $P = P_0(1 - r)^t$, where $P$ is the final population, $P_0$ is the initial population, $r$ is the rate of decrease (as a decimal), and $t$ is the time in years. Plugging in the given values, $2000 = 7700(1 - 0.19)^t$. Solving for $t$ gives approximately 7.75 years.

Question 7

At what quarterly compounded nominal interest rate will money double in 75 months?

Accepted Answer

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Question 8

At what annually compounded interest rate will an investment of $71,294.69 double in 90 months?

Accepted Answer

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Question 9

Sollozo just made a single payment to repay a loan he had with the Corleone Finance Company. He paid a total of $86,500 which included interest of $56,500 at 48% compounded monthly. How long ago was the money borrowed?

Accepted Answer

The interest formula for compound interest is A = P(1 + r/n)^(nt). Solving for t using the given values: A = $86,500, P = $30,000 (since $86,500 - $56,500 = $30,000), r = 0.48, n = 12, we find t ≈ 27 months.

Question 10

A $50,000 strip bond was discounted to $21,680. The market rate was 7.4% compounded semi-annually. How much time was left before the bond reached maturity?

Accepted Answer

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Question 11

Maury invested $5,000 in a selection of high-tech stocks. After six years of careful trading, his investments were worth $79,700. At what quarterly compounded nominal rate did his investments grow?

Accepted Answer

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Question 12

A six-year, $20,000 GIC has a maturity value of $29,625. Calculate the semi-annually compounded nominal interest rate.

Accepted Answer

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Question 13

At 11.4% compounded quarterly, how long will it take for money to double?

Accepted Answer

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Question 14

A $50,000 GIC will earn $70,000 of interest over its 10-year term. What is the monthly compounded nominal rate of interest?

Accepted Answer

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Question 15

The Wilsons bought their home 16 years ago for $128,000. Its value now is $141,000. At what annual rate has the value of their home appreciated since they bought it?

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Question 16

Rounded to the nearest month, how long will it take for $25,000 to grow to $35,000 at 9% compounded quarterly?

Accepted Answer

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Question 17

What amount invested at 10% compounded semiannually will be worth $6380.00 after 38 months?

Accepted Answer

To find the initial amount invested (the principal, P), we use the formula for compound interest: A = P(1 + r/n)^(nt), 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), 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 A = $6380, r = 10% or 0.10, n = 2 (since it's compounded semiannually), and t = 38 months or 38/12 years, we solve for P. Rearranging the formula to solve for P gives P = A / (1 + r/n)^(nt). Substituting the given values and solving for P gives the correct answer.

Question 18

Seven years before it matures the value of a $1,000 strip bond is $672. What is the semi-annually compounded nominal interest rate?

Accepted Answer

The value of a strip bond can be calculated using the formula for the present value of a single future amount: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods. Here, $PV = $672$, $FV = $1,000$, and $n = 7 \times 2 = 14$ periods (since the interest is compounded semi-annually). Rearranging the formula to solve for r gives us $r = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1$. Plugging in the values gives $r = \left(\frac{1000}{672}\right)^{\frac{1}{14}} - 1 \approx 0.0288$ per period, or $2.88\%$ per semi-annual period. Since the nominal annual interest rate is the semi-annual rate multiplied by 2, the nominal annual interest rate is $2.88\% \times 2 = 5.76\%$.

Question 19

At 14% compounded annually, an investment of $50,000 will grow to $1,000,000 in 22.86 years. How much longer will it take at 11% compounded annually?

Accepted Answer

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Question 20

What is the term of a compound-interest Guaranteed Investment Certificate if $8,500 invested at 6.1% compounded annually will earn interest totaling $4,365.50?

Accepted Answer

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Quiz 9: Compound Interest: Further Topics and Applications