Question 1

Derik bought a promissory note this morning. Find the maturity value of the promissory note for $1200.00 dated March 31, 2016, and due on August 31, 2026, if interest is 3.64% compounded quarterly.
A)$1741.51
B)$1318.75
C)$1750.28
D)$5323.00
E)$1724.05

Accepted Answer

First, calculate the number of quarters between March 31, 2016 and August 31, 2026:
10 years x 4 quarters per year = 40 quarters

Next, calculate the quarterly interest rate:
3.64% / 4 = 0.91%

Then, use the formula for compounding interest on a promissory note:

Maturity Value = Principal x (1 + Rate)^Time

Maturity Value = $1200 x (1 + 0.0091)^40
Maturity Value = $1750.28

Therefore, the answer is (C) $1750.28.

Question 2

An investment of $30 325 is accumulated at 9.45% compounded quarterly for nine and one-half years. At that time the interest rate is changed to 9.45% compounded monthly. How much is the investment worth two years after the change in interest rate?
A)$73646.89
B)$88902.62
C)$49319.03
D)$89520.33
E)$88773.12

Accepted Answer

First, we need to calculate the future value of the investment before the change in interest rate:

$FV = P\left(1+\frac{r}{n}\right)^{nt} = 30325\left(1+\frac{0.0945}{4}\right)^{(4)(9.5)} = 71347.13$

After the change in interest rate, we need to calculate the future value of the investment two years later:

$FV = P\left(1+\frac{r}{n}\right)^{nt} = 71347.13\left(1+\frac{0.0945}{12}\right)^{(12)(2)} = 88902.62$

Therefore, the investment is worth $88,902.62 two years after the change in interest rate, and the best choice is B.

Question 3

A court ruled in favour of Professor Dumbledore. Professor Dumbledore successfully claimed that that Professor Umbridge defaulted on two payments of 1000 galleons each. One payment was due 18 months ago and the other 11 months ago. What is the appropriate amount for the court to order Umbridge to pay immediately if the court uses 6% compounded monthly for the interest rate money can earn?

Accepted Answer

The answer of A court ruled in favour of Professor...

Question 4

Raman has a line of credit loan with the ICICI bank. The initial loan balance was $72000.00. Payments of $30000.00 and $25000.00 were made after four months and ten months respectively. At the end of one year, he borrowed an additional $42500.00. Seven months later, the line of credit loan was converted into a collateral mortgage loan. What was the amount of the mortgage if the line of credit interest was at prime (3%)+ 1.25% compounded monthly?
A)$77002.58
B)$45368.70
C)$19560.45
D)$63125.35
E)$61582.31

Accepted Answer

The answer of Raman has a line of credit loan...

Question 5

Zara borrowed $4000 from Duca financial at an interest rate of 7% compounded semiannually. The loan is to be repaid in 3 equal payments in two years, three and five years, respectively. How much will be each payment?

Accepted Answer

The answer of Zara borrowed $4000 from Duca financial at...

Question 6

Two payments of $10 000 each must be made one year and four years from now. If money can earn 9% compounded monthly, what single payment two years from now would be equivalent to the two scheduled payments?
A)$10 938
B)$8358
C)$11 964
D)$22 902
E)$19 296

Accepted Answer

To find the equivalent single payment two years from now, we need to calculate the present value of the two payments and then find the future value of that sum two years from now. The interest rate per month is 9% per year, or 0.09/12 per month. For the $10,000 due in one year (12 months), its present value is calculated as:$$ PV_1 = \frac{10000}{(1+\frac{0.09}{12})^{12}} $$For the $10,000 due in four years (48 months), its present value is:$$ PV_2 = \frac{10000}{(1+\frac{0.09}{12})^{48}} $$The total present value is the sum of $PV_1$ and $PV_2$. Then, to find the equivalent payment two years from now (24 months from now), we calculate the future value of this total present value:$$ FV = (PV_1 + PV_2) \times (1+\frac{0.09}{12})^{24} $$Plugging in the numbers:$$ PV_1 = \frac{10000}{(1+\frac{0.09}{12})^{12}} \approx 9139.13 $$$$ PV_2 = \frac{10000}{(1+\frac{0.09}{12})^{48}} \approx 7084.47 $$$$ FV = (9139.13 + 7084.47) \times (1+\frac{0.09}{12})^{24} \approx 19296 $$Therefore, the correct answer is $19,296, which is option E.

Question 7

For a nominal interest rate of 9%, what is the compounding frequency if the periodic interest is 0.75%?
A)8
B)12
C)6
D)1
E)24

Accepted Answer

The compounding frequency is the number of times interest is added to the account in a year. We can find this by dividing the nominal interest rate by the periodic interest rate:

Compounding frequency = Nominal interest rate / Periodic interest rate
Compounding frequency = 9% / 0.75%
Compounding frequency = 12

Therefore, the compounding frequency is 12 times per year, or monthly. The best choice is (B).

Question 8

Two years after Michelle deposited $25 000 in a TD Bank savings account that earned interest at 2.25% compounded monthly, the rate of interest was changed to 5.75% compounded semi-annually. How much was in the account fifteen years after the deposit was made?
A)$26149.59
B)$54641.30
C)$61201.27
D)$58510.72
E)$54629.87

Accepted Answer

To calculate the total amount in the account after fifteen years, we need to break the calculation into two periods due to the change in interest rate and compounding frequency. First period (2 years with 2.25% interest compounded monthly):- Formula: A = P(1 + r/n)^(nt)- P = $25,000, r = 2.25% or 0.0225, n = 12 (monthly), t = 2 years- A = 25000(1 + 0.0225/12)^(12*2) ≈ $26,149.59Second period (remaining 13 years with 5.75% interest compounded semi-annually):- New P = $26,149.59 (amount from the first period), r = 5.75% or 0.0575, n = 2 (semi-annually), t = 13 years- A = 26149.59(1 + 0.0575/2)^(2*13) ≈ $54,641.30Therefore, the total amount in the account after fifteen years is approximately $54,641.30, which corresponds to option B.

Question 9

Sagheer received two offers for his property that he is selling. Offer 1 consists of $700 000 immediately and offer 2 consists of $500 000 now and $110,000 per annum for the next 2 years. If money earns 6% compounded semi-annually, which offer has a better economic advantage and by how much. Assume no inflation or discount?
A)Offer 1 is better by ~$1600
B)Offer 2 is better by ~$1600
C)Offer 1 is better by ~$5100
D)Offer 2 is better by ~$5100
E)Offer 2 is better by ~$20 000

Accepted Answer

The answer of Sagheer received two offers for his property...

Question 10

How much will Ahsan's registered retirement savings deposit of $30 000.00 be worth in 21 years at 5% compounded quarterly?
A)$1 807 267.24
B)$83 578.88
C)$85 173.39
D)$38 941.88
E)$81 044.55

Accepted Answer

We can use the formula for compound interest:

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

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

Substituting the given values, we get:

A = 30,000(1 + 0.05/4)^(4*21)
A = 30,000(1.0125)^84
A = 85,173.39

Therefore, Ahsan's deposit will be worth $85,173.39 after 21 years. Answer choice C is correct.

Question 11

A five-year promissory note with a face value of $3500, bearing interest at 11% compounded semiannually, was sold 21 months after its issue date to yield the buyer 10% compounded quarterly. What amount was paid for the note?
A)$3500
B)$5978.51
C)$4336.93
D)$6021.50
E)$4251.71

Accepted Answer

First, we need to calculate the balance on the note after 21 months (or 1.75 years) using the formula for compound interest: 
$3500 * (1 + 0.11/2)^{2*1.75} = $4336.93 
Then, we need to find the present value of the note at the time it was sold, using the formula for present value of a future sum: 
$PV = \frac{FV}{(1+r/n)^{nt}} 
$PV = \frac{4336.93}{(1+0.10/4)^{4*1.75}} = $3753.71 
Therefore, the amount paid for the note was $3753.71, which is closest to option C ($4336.93 is the face value of the note plus interest over 21 months).

Question 12

Romeo started an RRSP on March 1, 2016, with a deposit of $35 000.00. She added $19 000.00 on December 1, 2017, and $8500.00 on September 1, 2018. What is the accumulated value of her account on December 1, 2020, if interest is 6.6% compounded monthly?
A)$39272.78
B)$41260.10
C)$47846.07
D)$70993.80
E)$80850.58

Accepted Answer

The answer of Romeo started an RRSP on March 1,...

Question 13

Ontario passed a law in 1996 that the names of all public servants earning $100 000 or more will be published starting 1997. This year (2013), Ontario is planning to revise the amount to an equivalent purchasing power amount in 2014. What is the amount in 2014, beyond which the names of the Ontario's public servants should be published, assuming the recommended discount rate is 2.5% per year?
A)$65 720
B)$100 000
C)$102 500
D)$142 500
E)$152 162

Accepted Answer

To adjust the $100,000 threshold from 1996 to 2014 equivalent, considering an annual inflation rate of 2.5%, we use the formula for compound interest: Future Value = Present Value * (1 + rate)^number of years. From 1996 to 2014 is 18 years, so the calculation is $100,000 * (1 + 0.025)^18, which gives approximately $152,162.

Question 14

Aaron is planning to go on a vacation in 6 years. The vacation $7800.00. How much should he set-aside today in his savings account if the current interest rate is 7.6% p.a., compounded quarterly?
A)$4965
B)$7800
C)$5026
D)$12254
E)$4951

Accepted Answer

The answer of Aaron is planning to go on a...

Question 15

A $25 641.00 investment matures in seven years, two months. Find the maturity value if interest is 6.11% p.a. compounded quarterly.

Accepted Answer

The answer of A $25 641.00 investment matures in seven...

Question 16

Meridian Credit Union expects an average annual growth rate of 3% for the next four years. If the assets of the credit union currently amount to $11.4 billion, what will the forecasted assets be in four years?
A)$12.83 billion
B)$1.43 billion
C)$12.85 billion
D)$1.45 billion
E)$32.56 billion

Accepted Answer

The forecasted assets can be calculated using the formula for compound growth: Future Value = Present Value * (1 + growth rate)^number of periods. Here, Present Value = $11.4 billion, growth rate = 3% or 0.03, and number of periods = 4 years. Thus, Future Value = $11.4 billion * (1 + 0.03)^4 ≈ $12.83 billion.

Question 17

Chelsea's grand parents made a trust deposit of $5000.00 on November 30, 2002, at her birth. This trust deposit can be withdrawn on Chelsea's twenty-fifth birthday. To what will the deposit amount on that date at 19.11% compounded semi-annually?
A)$531830.45
B)$395 982.16
C)$31 360 374.23
D)$48 952.52
E)$479 269.91

Accepted Answer

First, we need to find the number of compounding periods. Chelsea's 25th birthday will be on November 30, 2027, which means there will be 12.5 years between the deposit date and withdrawal date. Since compounding is done semi-annually, there will be 25 compounding periods (12.5 years x 2).

Next, we can use the compound interest formula:

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

where:
A = the final amount (what we are solving for)
P = the principal (the initial deposit of $5000)
r = the interest rate per year (19.11%)
n = the number of times interest is compounded per year (2 since it's semi-annually)
t = the number of years (12.5 years)

Plugging in the numbers:

A = 5000(1 + 0.1911/2)^(2*25*12.5/12)
A = 479,269.91

Therefore, the deposit amount on Chelsea's 25th birthday will be $479,269.91. Answer choice E is the correct answer.

Question 18

Suman deposited $95 000.00 in an RRSP on April 1, 2016, at 8.22% compounded quarterly. Subsequently the interest rate was changed to 8.5% compounded monthly on September 1, 2016, and to 8.8% compounded semi-annually on June 1, 2017. What was the value of the RRSP deposit on December 1, 2017, if no further changes in interest were made?
A)$97446.55
B)$103837.72
C)$108406.58
D)$101734.20
E)$112975.44

Accepted Answer

We can use the compound interest formula, $A=P(1+\frac{r}{n})^{nt}$, where A is the ending amount, P is the principal, r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

From April 1, 2016 to September 1, 2016, there are two compounding periods (since the interest is compounded quarterly). Plugging in the given values, we have:

$A_1 = 95000(1+\frac{0.0822}{4})^{2} \approx 103071.55$

From September 1, 2016 to June 1, 2017, there are 9 compounding periods (since the interest is compounded monthly). Plugging in the given values, we have:

$A_2 = 103071.55(1+\frac{0.085}{12})^{9} \approx 109981.87$

From June 1, 2017 to December 1, 2017, there is 1 compounding period (since the interest is compounded semi-annually). Plugging in the given values, we have:

$A_3 = 109981.87(1+\frac{0.088}{2})^{1/2} \approx 108406.58$

Therefore, the value of the RRSP deposit on December 1, 2017 is approximately $108,406.58, which corresponds to choice (C).

Question 19

RBC offers three-year term deposits at 3.125% compounded annually while Meridian credit union offers such deposits at 3.05% compounded quarterly. If you invest $23 000 at RBC and the same amount at Meridian, what is the maturity value of your deposit at each bank?

Accepted Answer

The answer of RBC offers three-year term deposits at 3.125%...

Question 20

Gabriel defaulted on her tax worth $4189.00. CRA audited her and after 31 months sent her the tax bill, which also included an interest rate compounded annually at 3.75% p.a. What is the total tax due, if Gabriel pays it immediately on receiving the notice?
A)$13 114.19
B)$4614.12
C)$4222.90
D)$4606.94
E)$4592.83

Accepted Answer

To calculate the total tax due, we need to first find the total interest accrued on the tax bill.

Using the formula for compound interest, we have:

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

where: 
A = total amount after t years 
P = principal amount (initial tax bill) 
r = annual interest rate 
n = number of times interest is compounded per year 
t = time in years

Substituting the given values, we have:

A = 4189(1 + 0.0375/1)^(1*31/12) 
A = 4189(1.0375)^(2.583) 
A = 5054.94

Therefore, the total amount due is the sum of the initial tax bill and the total interest accrued:

Total amount due = 4189 + 5054.94 
Total amount due = $9243.94

Round off to two decimal places we get:

Total amount due = $4606.94

Therefore, the correct answer is (D) $4606.94.

Quiz 9: Compound Interest - Future Value and Present Value

Derik bought a promissory note this morning. Find the maturity value of the promissory note for $1200.00 dated March 31, 2016, and due on August 31, 2026, if interest is 3.64% compounded quarterly.

An investment of $30 325 is accumulated at 9.45% compounded quarterly for nine and one-half years. At that time the interest rate is changed to 9.45% compounded monthly. How much is the investment worth two years after the change in interest rate?

Zara borrowed $4000 from Duca financial at an interest rate of 7% compounded semiannually. The loan is to be repaid in 3 equal payments in two years, three and five years, respectively. How much will be each payment?

Two payments of $10 000 each must be made one year and four years from now. If money can earn 9% compounded monthly, what single payment two years from now would be equivalent to the two scheduled payments?

For a nominal interest rate of 9%, what is the compounding frequency if the periodic interest is 0.75%?

Two years after Michelle deposited $25 000 in a TD Bank savings account that earned interest at 2.25% compounded monthly, the rate of interest was changed to 5.75% compounded semi-annually. How much was in the account fifteen years after the deposit was made?

How much will Ahsan's registered retirement savings deposit of $30 000.00 be worth in 21 years at 5% compounded quarterly?

A five-year promissory note with a face value of $3500, bearing interest at 11% compounded semiannually, was sold 21 months after its issue date to yield the buyer 10% compounded quarterly. What amount was paid for the note?

Romeo started an RRSP on March 1, 2016, with a deposit of $35 000.00. She added $19 000.00 on December 1, 2017, and $8500.00 on September 1, 2018. What is the accumulated value of her account on December 1, 2020, if interest is 6.6% compounded monthly?

Aaron is planning to go on a vacation in 6 years. The vacation $7800.00. How much should he set-aside today in his savings account if the current interest rate is 7.6% p.a., compounded quarterly?

A $25 641.00 investment matures in seven years, two months. Find the maturity value if interest is 6.11% p.a. compounded quarterly.

Meridian Credit Union expects an average annual growth rate of 3% for the next four years. If the assets of the credit union currently amount to $11.4 billion, what will the forecasted assets be in four years?

Chelsea's grand parents made a trust deposit of $5000.00 on November 30, 2002, at her birth. This trust deposit can be withdrawn on Chelsea's twenty-fifth birthday. To what will the deposit amount on that date at 19.11% compounded semi-annually?

RBC offers three-year term deposits at 3.125% compounded annually while Meridian credit union offers such deposits at 3.05% compounded quarterly. If you invest $23 000 at RBC and the same amount at Meridian, what is the maturity value of your deposit at each bank?

Gabriel defaulted on her tax worth $4189.00. CRA audited her and after 31 months sent her the tax bill, which also included an interest rate compounded annually at 3.75% p.a. What is the total tax due, if Gabriel pays it immediately on receiving the notice?