Loan table – Annuity – Quarterly: 13 Corrected exercises

Welcome to this article whose sole purpose is to help you progress in the chapter entitled financing investments using corrected exercises from the Operational Management subject of the BTS MCO.

This theme of corrected exercises Borrowing table was created to master all the possibilities of calculating the financing of investments.

If you would like to first watch or review the course on investment financing, I invite you to read my article

Lesson 7 corrected exercises on the loan board of this page mainly concern the borrowing table and the constant annuity.

You will also find corrected exercises on the following concepts: the calculation of the constant annuity, the calculation of quarterly constant annuities, the calculation of half-yearly and monthly constant annuities.

Here is the list of the 13 corrected exercises on the borrowing table:

1. Exercise No. 1: Loan table – Repayment by constant amortization
2. Exercise No. 2: Borrowing table – Repayment by constant annuities
3. Exercise No. 3: Calculation of proportional monthly rate
4. Exercise No. 4: Calculating the half-yearly payment of a loan
5. Exercise No. 5: loan table – Repayment by constant amortizations
6. Exercise No. 6: Amortization table – Repayment by constant annuities
7. Exercise No. 7: Calculation of the constant annuity
8. Exercise No. 8: Calculation of a constant monthly payment
9. Exercise No. 9: Calculation of a constant quarterly
10. Exercise No. 10: Calculation of a constant half-yearly rate
11. Exercise No. 11: Extract from the amortization table
12. Exercise No. 12: Extract from the Borrowing Table – Constant Semester Payments
13. Exercise No. 13: Extract from the Borrowing Table – Constant Quarterly Payments

Corrected exercises Borrowing table No. 1: Repayment by constant amortizations

States

The Ide business unit manufactures and sells costumes for all audiences: young and old, individuals and professionals.

Mr Lecas, the head of the business unit, wants to invest in new premises worth €365.

For this reason, he gives you information regarding the financing method to provide answers to his questions.

Funding method :

• Type of financing: Loan;
• Interest rate: 6% per year;
• Amount borrowed: Amount of the premises;
• Repayment period: 4 years.
• Reimbursement type: Constant depreciation

Work to do

1. Present the loan amortization plan.

Corrected exercise No. 1

(1): Capital remaining due at the start of the period multiplied by the interest rate

so: 365 × 000

(2): This is a constant amortization repayment method so you must divide the loan amount by the number of periods

so: 365 ÷ 000

(3): the calculation of the annuity is equal to the sum of the interest and the amortization

so: Interest + Amortization for each line or 21 + 900

(4): the remaining capital due at the end of the period only takes into account the amortization amounts of the line

therefore: capital remaining due at the start of the period – Amortization i.e. 365 – 000

Corrected exercises Loan table No. 2: Repayment by constant annuities

States

The Lepin business unit specializes in the production of breads and cakes.

Its products are intended for both individuals and professionals.

The company wants to invest in a new oven, for an amount of €150 excluding tax, but is unsure about the financing method.

Its manager, Mr. Lalevure, will provide you with certain information relating to the financing method.

Funding method :

• Type of financing: Loan;
• Interest rate: 4,5% per year;
• Amount borrowed: Amount of investment;
• Repayment period: 5 years.
• Repayment Type: Constant Annuities

Work to do

1. Present the loan amortization plan.

Corrected exercise No. 2

First of all it is necessary to calculate the amount of the constant annuity before creating the requested table.

For this we will apply the following formula:

a = V₀ × [i ÷ (1 – (1+i)^-n)]

So:

a = 150 × [000 ÷ (0,045 – (1 + 1)^-5)]

From which a = €34

(1): To calculate interest, you must multiply the outstanding principal by the interest rate.

so: 150 × 000

(2): To calculate the amortization amount, you must subtract the interest amount from the constant annuity amount.

so: (3) – (1) or 34 – 168,74

(3): To calculate the constant annuity, you must apply the formula seen above and copy the result

(4): the remaining capital due at the end of the period only takes into account the amortization amounts of the line

therefore: capital remaining due at the start of the period – Amortization i.e. 150 – 000

Corrected exercises Borrowing table No. 3: Calculation of proportional monthly rate

States

The Lesson business unit wishes to borrow capital of €135 in order to finance an investment project.

We send you the banking conditions in appendix 1.

Annexe 1 : Banking conditions

Annual interest rate: 5,75%

Frequency of repayments: Monthly

Work to do

1. Calculate the monthly proportional rate.

Corrected exercise No. 3

In this exercise it is necessary to calculate the proportional monthly rate because the repayment frequency and the periodicity of the rate are different.

Calculation of the monthly proportional rate:

Rate = 5,75% / 12 or 0,48%

The monthly proportional rate is therefore 0,48%.

If you want to calculate the amount of the constant monthly payment, you just need to apply the constant annuity formula but taking into account the proportional monthly rate and a number of months and not years.

Exercise No. 4: Calculating the half-yearly payment of a loan

States

The Cayo business unit specializes in the distribution of medical equipment for hospitals.

She wants to invest in new technology (€125 excluding tax) but is unsure about the banking conditions.

In fact, she wants to borrow because the investment amount is very large.

The company wants to repay the entire amount over 5 years.

Annexe 1 : Banking conditions

Annual interest rate: 5,75%

Frequency of repayments: Half-yearly

Work to do

1. Calculate the half-yearly repayment of the loan.

Corrected exercise No. 4

In this exercise it is necessary to calculate the proportional half-yearly rate because the repayment frequency and the periodicity of the rate are different.

Calculation of the proportional half-yearly rate:

Rate = 5,75% ÷ 2 (2 semesters) or 2,875%

The proportional half-yearly rate is therefore 2,875%.

If one wishes to calculate the amount of the constant semi-annual payment, one simply needs to apply the constant annuity formula but taking into account the proportional semi-annual rate and a number of semesters and not years.

So we have:

Calculation of the number of semesters: 5 years x 2 semesters = 10 semesters

So we have :

125 × [000 ÷ (0,02875 – (1 + 1)^-10] = 14 560,48 €

The amount of the half-yearly payment is therefore 14 560,48 €.

Corrected exercises Borrowing table No. 5: Constant amortization

States

The following elements are given:

Loan amount in N: €20

Annual rate: 6,5%

Repayment Type: Constant Amortization

Loan term: 5 years

Work to do

1. Present the loan repayment schedule.

Corrected exercise No. 5

? : postponement of ?

? : ? x 0,065

? : 20 ÷ 000 years

? : ? + ?

? : ? – ?

Corrected exercises Loan table No. 6: Repayment by constant annuities

States

The following elements are given:

Loan amount in N: €10

Annual rate: 4,5%

Repayment Type: Constant Annuities

Loan term: 5 years

Work to do

1. Present the loan repayment schedule.

Corrected exercise No. 6

First, you need to calculate the amount of the constant annuity by applying the following formula:

Loan × [interest rate ÷ (1 – (1 + interest rate)^-n)]

So we have the following calculation:

10 × [000 ÷ (0,045 – (1 + 1)^-5)] = €2

We can now create the requested table:

? : postponement of ?

? : ? × 0,045

? : ? – ?

? : according to calculation of the constant annuity

? : ? – ?

Corrected exercises Borrowing table No. 7: Calculation of a constant annuity

States

The following elements are given:

Loan amount in N: €15

Annual rate: 3,5%

Repayment Type: Constant Annuities

Loan term: 5 years

Work to do

1. Calculate the amount of the constant annuity.

Corrected exercise No. 7

To accomplish the requested work, we will use the following formula:

Loan × [interest rate ÷ (1 – (1 + interest rate)^-n)]

So we have:

15 × [000 ÷ (0,035 – (1 + 1)^-5)] = €3

The amount of the constant annuity is therefore €3.

Corrected exercises Loan table No. 8: Calculation of a constant monthly payment

States

The following elements are given:

Loan amount in N: €35

Monthly rate: 0,54%

Repayment type: Constant monthly payments

Loan term: 5 years

Work to do

1. Calculate the amount of the constant annuity.

Corrected exercise No. 8

In this corrected exercise, the calculation does not pose any particular problem.

You just have to adapt the number of periods (5 years x 12 months = 60 months) by taking the following constant annuity formula:

Loan × [interest rate ÷ (1 – (1 + interest rate)^-n)]

So we have the following calculation:

35 × [000 ÷ (0,0054 – (1 + 1)^-60)] = €684,49

The amount of the constant monthly payment is therefore €684,49.

Corrected exercises Borrowing table No. 9: Calculation of a constant quarterly

States

The following elements are given:

Loan amount in N: €65

Quarterly rate: 0,65%

Reimbursement type: Constant quarterly payments

Loan term: 5 years

Work to do

1. Calculate the amount of the constant quarterly.

Corrected exercise No. 9

In this corrected exercise, care must be taken to adapt the constant annuity formula according to the number of months.

In fact, these are constant quarterly payments.

In five years there are 5 x 4 quarters, making a total of 20 quarters.

The formula to adapt is as follows:

Loan × [interest rate ÷ (1 – (1 + interest rate)^-n)]

So we have:

65 × [000 ÷ (0,065 – (1 + 1)^-20)] = €3

The amount of the constant quarterly payment is therefore €3.

Corrected exercises Borrowing table No. 10: Calculation of a constant semester

States

The following elements are given:

Loan amount in N: €65

Half-yearly rate: 0,65%

Reimbursement type: Constant half-yearly payments

Loan term: 5 years

Work to do

1. Calculate the amount of the constant half-yearly payment.

Corrected exercise No. 10

In this exercise, the constant annuity formula must be adapted because we are dealing here with half-yearly payments and not constant annuities.

We will therefore transform the following formula by specifying a number of periods equal to 5 years x 2 semesters, i.e. a total of 10 semesters over the period:

Loan × [interest rate ÷ (1 – (1 + interest rate)^-n)]

So we have the following calculation:

65 × [000 ÷ (0,0065 – (1 + 1)^-10)] = €6

The amount of the constant half-yearly payment is therefore €6.

Corrected exercises Loan table No. 11: Extract from Loan table – Constant monthly payments

States

The following elements are given:

Loan amount in N: €25

Monthly rate: 1,5%

Repayment type: Constant monthly payments

Loan term: 5 years

Work to do

1. Present the first 3 lines of the loan repayment table.

Corrected exercise No. 11

First, it is necessary to calculate the amount of the constant monthly payment by adapting the following formula:

Loan × [interest rate ÷ (1 – (1 + interest rate)^-n)]

So we have:

25 × [000 ÷ (0,015 – (1 + 1)^-60)] = €634,83

The amount of the constant monthly payment is therefore €634,83.

? : postponement of ?

? : ? × 0,015

? : ? – ?

? : according to calculation of the constant monthly payment

? : ? – ?

Corrected exercises Borrowing table No. 12: Extract Borrowing table – Constant semesters

States

The following elements are given:

Loan amount in N: €45

Half-yearly rate: 1,75%

Reimbursement type: Constant half-yearly payments

Loan term: 6 years

Work to do

1. Present the first 3 lines of the loan repayment table.

Corrected exercise No. 12

First, it is necessary to calculate the amount of the constant half-yearly payment by adapting the following formula:

Loan × [interest rate ÷ (1 – (1 + interest rate)^-n)]

So we have:

45 × [000 ÷ (0,0175 – (1 + 1)^-12)] = €4

The amount of the constant half-yearly payment is therefore €4.

? : postponement of ?

? : ? × 0,0175

? : ? – ?

?: according to calculation of the constant half-yearly rate

? : ? – ?

Corrected exercises Borrowing table No. 13: Extract Borrowing table – Constant quarterly payments

States

The following elements are given:

Loan amount in N: €45

Quarterly rate: 2,95%

Reimbursement type: Constant quarterly payments

Loan term: 9 years

Work to do

1. Present the first 3 lines of the loan repayment table.

Corrected exercise No. 13

Firstly, it is necessary to calculate the amount of the constant quarterly payment by adapting the following formula:

Loan × [interest rate ÷ (1 – (1 + interest rate)^-n)]

So we have:

There are 9 x 4 quarters over the 9-year period, making a total of 36 quarters.

45 × [000 ÷ (0,0295 – (1 + 1)^-36)] = €2

The amount of the constant quarterly payment is therefore €2.

? : postponement of ?

? : ? × 0,0295

? : ? – ?

?: according to calculation of constant quarterly

? : ? – ?