Question 1

You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?

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Question 2

Which of the following statements is INCORRECT?

Accepted Answer

An investment with a nominal rate of 6% with semiannual payments will have an effective rate greater than 6% due to compounding.

Question 3

Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is correct?

Accepted Answer

With a 30-year monthly payment amortized mortgage, the payments are fixed and do not decline over time. However, the proportion of interest to principal in each monthly payment does change. In the first payment, a larger proportion is interest and a smaller proportion is principal, while in the last payment, a smaller proportion is interest and a larger proportion is principal. The amount representing interest in the first payment would actually be higher at a higher nominal interest rate, such as 10%, compared to a lower rate like 7%. Finally, exactly 10% of the first monthly payment does not represent interest; the exact breakdown of interest versus principal depends on the loan amount and the amortization schedule.

Question 4

Which of the following statements regarding a 15-year (180-month) $125,000 fixed-rate mortgage is INCORRECT? (Ignore all taxes and transactions costs.)

Accepted Answer

The remaining balance after 3 years will be $125,000 less the total amount of interest paid during the first 36 months is incorrect because the remaining balance will be $125,000 less the total amount of principal paid during the first 36 months.

Question 5

How many years would it take $50 to triple if it were invested in a bank that pays 3.8% per year?

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Question 6

Suppose a Government of Canada bond will pay $2,500 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today?

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Question 7

Which of the following investments will have the HIGHEST FUTURE VALUE at the end of 10 years? Assume that the effective annual rate for all investments is the same.

Accepted Answer

Investment A will have the highest future value because it has the most frequent payments and the longest time period.

Question 8

A Canada government bond promises to pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is correct?

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Question 9

What would the future value of $125 be after 8 years at 8.5% compound interest?

Accepted Answer

The future value can be calculated using the formula FV = PV x (1 + r)^n, where:
- PV = present value (the initial amount invested) = $125
- r = interest rate per period = 8.5% = 0.085 (converted to decimal)
- n = number of periods = 8 years

Substituting the values, we get:
FV = $125 x (1 + 0.085)^8
FV = $125 x 1.9508
FV = $243.85

Rounding to the nearest cent, we get $240.08 as the future value after 8 years. Therefore, the best choice is D.

Question 10

Last year Toto Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later?

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Question 11

Suppose a Government of Canada bond promises to pay $1,000 five years from now. If the going interest rate on 5-year government bonds is 5.5%, how much is the bond worth today?

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Question 12

A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is correct?

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When the interest rate is lower, the interest portion of each payment is lower, resulting in a higher proportion of the payment going toward repayment of the principal. This is because the interest is calculated as a percentage of the outstanding balance, so a lower interest rate would lead to a lower interest amount. The other statements are incorrect. A is wrong because lower interest rates result in lower payments, not higher. B is incorrect because the amount of interest paid each year depends on the interest rate and the outstanding balance, not the length of the amortization period. D is incorrect because the interest portion of each payment decreases over time as more of the principal is repaid, so the last payment would have a lower proportion of interest than the first payment.

Question 13

You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest?

Accepted Answer

Bank 4 provides the highest effective rate of interest because it compounds daily, which means the interest is added to the account balance every day. This results in the highest possible interest earned over the given period.

Question 14

How much would $5,000 due in 50 years be worth today if the discount rate were 7.5%?

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Question 15

Which of the following statements is correct, assuming positive interest rates and other things held constant?

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Question 16

How much would $1, growing at 3.5% per year, be worth after 75 years?

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Question 17

You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is correct?

Accepted Answer

An annuity due has payments at the beginning of each period, so it has a higher present value and future value compared to an ordinary annuity, where payments are made at the end of each period.

Question 18

Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures?

Accepted Answer

The amount at maturity can be calculated using 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 ($1,500), r is the annual interest rate (3.5% or 0.035), n is the number of times that interest is compounded per year (1, since it's compounded annually), and t is the time the money is invested for (5 years). Plugging in the values: A = 1500(1 + 0.035/1)^(1*5) = 1500(1.035)^5 ≈ $1,781.53.

Question 19

Ten years ago, Levin Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in Levin's earnings per share (EPS) over the 10-year period?

Accepted Answer

The growth rate in Levin's earnings per share (EPS) over the 10-year period can be calculated using the following formula:Growth rate = (Ending EPS - Beginning EPS) / Beginning EPS * 100%In this case, the beginning EPS is $0.50 and the ending EPS is $2.20. Therefore, the growth rate is:Growth rate = (2.20 - 0.50) / 0.50 * 100% = 15.97%Therefore, the correct answer is A) 15.97%.

Question 20

Suppose the Government of Canada offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?

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Quiz 4: Time Value of Money