Topic 1.7: Amortisation and Annuities Questions

Beatriz borrows €20000 from a bank at a nominal annual interest rate of 6.6%, compounded monthly. She repays in equal monthly instalments at the end of each month over 4 years.

Carlos deposited $50 000 into a savings account with a nominal annual interest rate of I% compounded monthly. At the end of the sixth year, the balance had grown to $68 000.

In this question, give all monetary answers to two decimal places unless stated otherwise.

Ingrid wants to buy a car for a price of 450 000 Norwegian krone (NOK). She goes to a bank to get a loan. To be eligible, Ingrid must make an initial down payment equal to 20 % of the price of the car.

The bank offers her a 5-year loan for the remaining balance, with a 4.8 % nominal interest rate per annum, compounded monthly. Ingrid will pay the loan in fixed payments at the end of each month.

Ingrid would like to repay the loan faster and increases her payments such that she pays 7 500 NOK each month.

Nina takes out a loan of $12000 at a nominal annual interest rate of 9.6%, compounded monthly. The loan is to be repaid in equal monthly instalments at the end of each month over 3 years. Calculate the monthly instalment. Give your answer correct to the nearest cent.

Amara takes out a loan of $22000 at a nominal annual interest rate of 10.8%, compounded monthly. The loan is repaid in equal monthly instalments over 6 years. Calculate the total interest paid over the lifetime of the loan.

Yuki takes out a personal loan of $15000 at a nominal annual interest rate of 7.8%, compounded monthly. She repays the loan in equal monthly instalments at the end of each month over 5 years.

Aria wants to buy an apartment priced at 260 000 AUD. She pays 22% upfront and borrows the rest over 10 years with monthly payments of 1 950 AUD at the end of each month.

In this question, give all monetary answers to two decimal places unless stated otherwise.

Priya wants to buy a new scooter for a price of 180 000 Indian rupees (INR). She visits a bank to arrange a loan. To be eligible, Priya must make an initial down payment equal to 15 % of the price of the scooter.

The bank offers her a 3-year loan for the remaining balance, with a 9.6 % nominal interest rate per annum, compounded monthly. Priya will pay the loan in fixed payments at the end of each month.

Priya would like to repay the loan faster and increases her payments such that she pays 5 500 INR each month.

David wants to buy a motorbike costing $8 800. He pays $1 800 as a deposit. For the remainder he takes out a loan from a bank.

(a) Write down the amount of money that David takes out as a loan. [1]

The loan is for 3 years and the nominal annual interest rate is 9.0% compounded monthly. David will pay the loan in fixed monthly instalments at the end of each month.

(b) Calculate the amount, correct to the nearest dollar, that David will have to pay the bank each month. [3]

(c) Calculate the total interest David will pay over the full term of the loan. [2]

Elena wants to buy a car costing $22 000. She uses $4 500 of her savings as a deposit. For the remainder she takes out a loan from a bank.

(a) Write down the amount of money that Elena takes out as a loan. [1]

The loan is for 5 years and the nominal annual interest rate is 11.4% compounded monthly. Elena will pay the loan in fixed monthly instalments at the end of each month.

(b) Calculate the amount, correct to the nearest dollar, that Elena will have to pay the bank each month. [3]

(c) Calculate the total interest Elena will pay over the full term of the loan. [2]

Miguel wants to buy a used car costing $14 500. He uses $3 500 of his savings as a deposit. For the remainder he takes out a loan from a bank.

(a) Write down the amount of money that Miguel takes out as a loan. [1]

The loan is for 4 years and the nominal annual interest rate is 8.4% compounded monthly. Miguel will pay the loan in fixed monthly instalments at the end of each month.

(b) Calculate the amount, correct to the nearest dollar, that Miguel will have to pay the bank each month. [3]

(c) Calculate the total interest Miguel will pay over the full term of the loan. [2]

Using the same loan from the previous question (principal 202 800 AUD, monthly payment 1 950 AUD, annual nominal rate 2.91% compounded monthly), Aria considers clearing the loan after 5 years with one payment.

In this question, give all monetary answers to two decimal places unless stated otherwise.

Kwame wants to buy a commercial truck for a price of 120 000 Ghanaian cedis (GHS). He visits a bank to arrange a loan. To be eligible, Kwame must make an initial down payment equal to 30 % of the price of the truck.

The bank offers him a 4-year loan for the remaining balance, with an 18 % nominal interest rate per annum, compounded monthly. Kwame will pay the loan in fixed payments at the end of each month.

Kwame would like to repay the loan faster and increases his payments such that he pays 3 000 GHS each month.

Amara placed $200 000 into a fixed-term savings account with a nominal annual interest rate of I% compounded monthly. At the end of the tenth year, the balance had grown to $280 000.

Liu Wei deposited $120 000 into a pension savings account with a nominal annual interest rate of I% compounded monthly. At the end of nine years, the balance had grown to $195 000.

In this question, give all answers to two decimal places.

David decides to purchase photography equipment with a total price of €3 600. He cannot pay in full and the shop offers two loan options.

Finance option A:
A 2-year loan at a nominal annual interest rate of 18 % compounded monthly.
No deposit is required and repayments are made each month.

Finance option B:
A 2-year loan at a nominal annual interest rate of r % compounded quarterly.
The loan requires a 25 % deposit and quarterly repayments of €360.

David chooses option B. The shop invests the money David pays as soon as they receive it.

Kenji invests $4200 in a bank that pays a nominal annual interest rate of 1.5% compounded monthly.

In this question, give all answers to two decimal places.

Sofia decides to buy a new motorcycle with a price of €9 600, but cannot pay the full amount immediately. The dealership offers two options to finance the purchase.

Finance option A:
A 4-year loan at a nominal annual interest rate of 12 % compounded monthly.
No deposit is required and repayments are made each month.

Finance option B:
A 4-year loan at a nominal annual interest rate of r % compounded quarterly.
The loan requires a 10 % deposit and quarterly repayments of €230.

Sofia chooses option B. The dealership invests the money Sofia pays as soon as they receive it.

In this question, give all answers to two decimal places.

Marco decides to purchase a home appliance package costing €6 000. He cannot pay in full and the retailer offers two loan options.

Finance option A:
A 3-year loan at a nominal annual interest rate of 9 % compounded quarterly.
No deposit is required and repayments are made each quarter.

Finance option B:
A 3-year loan at a nominal annual interest rate of r % compounded monthly.
The loan requires a 15 % deposit and monthly repayments of €140.

Marco chooses option B. The retailer deposits Marco's payments into a savings account as soon as they are received.

In this question, give all answers to two decimal places.

Anika decides to buy a laptop and study equipment package costing €2 400. She cannot pay immediately and the campus bookshop offers two payment options.

Finance option A:
A 2-year loan at a nominal annual interest rate of 18 % compounded monthly.
No deposit is required and repayments are made each month.

Finance option B:
A 2-year loan at a nominal annual interest rate of r % compounded semi-annually.
The loan requires a 20 % deposit and semi-annual repayments of €520.

Anika chooses option B. The campus bookshop invests the money Anika pays as soon as they receive it.