I
I. Using Tables to solve problems with Fixed Term Deposits, Depreciation, and Loan Repayments
Websites to view:
Using the tables from NCSECU find out the following information:
Fixed rate account:
1. Say you had won the lottery and you received $1,000,000. If you invested this money in a CD at SECU, how much interest would you collect in
a) 36 months? __________b) 48 months? __________c) 60 months _________
If you win the lottery, could you live off the interest of 1,000,000? Are you really rich????
Personal Loans: You want to buy a car and you can only afford $350 a month for a payment. How much could you spend on a car if you took out a loan for the following time frames? How much interest would you be paying for the cars? Which car would you choose to purchase?
|Payment |Interest Rate |Amount of the car you |Amount of interest you |Final amount you would|
| | |could afford |would pay for the length |pay for the car. |
| | | |of the loan | |
|$350.00 | | | | |
|$350.00 | | | | |
|$350.00 | | | | |
Depreciation Tables: Let’s say you purchased a car for $20,000. Once you drive it off the lot you lose 20% of its value. How much is the car worth after 1 year? If it loses 10% of its value each year after that, how much will it be worth in 7 years? Make a table to show its value.
|Year |Amount of car |Amount of Depreciation |The value of the car |
|1 |$20,000 | | |
|2 | | | |
|3 | | | |
|4 | | | |
|5 | | | |
|6 | | | |
|7 | | | |
IB Sample Questions for this unit:
1. The table below shows the monthly repayments per $10 000 borrowed for various nominal annual interest rates.
|Loan term |Table of monthly repayments in $, per $10 000 |
|(years) |Annual interest rate |
| |7% |8% |9% |
|5 |198.0112 |202.7634 |207.5836 |
|10 |116.1085 |121.3276 |126.6758 |
|15 |89.8828 |95.5652 |101.4267 |
|20 |77.5299 |83.6440 |89.9726 |
|25 |70.6779 |77.1816 |83.9196 |
Beryl borrows $150 000 to buy an apartment at an interest rate of 8%, to be repaid over 20 years.
(a) Calculate Beryl’s exact monthly repayment.
(b) Find the exact amount of interest paid for the loan over the 20 years.
(Total 6 marks)
2. The following table shows the monthly payments needed to repay a loan of $1000 with various rates and time periods.
|Table of Monthly Repayments per $1000 |
|Annual interest rate |
|Loan Term |5% |5.5% |6% |6.5% |
|(months) | | | | |
|12 |87.50 |87.92 |88.34 |88.75 |
|18 |59.74 |60.21 |60.62 |61.12 |
|24 |45.94 |46.38 |46.84 |47.25 |
|30 |37.66 |38.11 |38.57 |39.04 |
|36 |32.16 |32.62 |33.09 |33.56 |
|42 |28.25 |28.72 |29.20 |29.70 |
|48 |25.33 |25.81 |26.30 |26.80 |
Sarah takes out a personal loan for $24 000 to buy a car. She negotiates a loan for three years at 6% per annum interest.
(a) Calculate the exact monthly repayment she will make.
(2)
(b) Find the exact total of the repayments she will make.
(2)
Beryl took out a loan of $10 000 for 18 months. The total she paid for the loan was $10 837.80.
(c) Find the rate of interest charged on the loan.
(2)
(Total 6 marks)
3. Mario has spent $40000 to buy some land. The land increases in value by 5% each year.
(i) What is the value of the land after the end of five years?
At the end of five years, Mario sells the land. He pays 1% tax on the sale and spends the rest of the money on a car. The car loses value at a rate of $2500 every year.
(ii) How much tax does Mario pay?
(iii) How much is the car worth five years after Mario buys it?
4. Bobby is spending a year traveling from America to France and Britain.
Consider the following exchange rates.
1 US dollar (USD) = 0.983 Euros
1 British Pound (GBP) = 1.59 Euros
(a) Bobby changes 500 USD into Euros.
(i) Calculate how many Euros he receives.
He spends 328 Euros in France and changes the remainder into GBP.
(ii) Calculate how many GBP he receives.
While in Britain Bobby decides to put this money in a bank that pays 6% simple interest per annum, and he gets a part-time job to cover his expenses. Bobby remains in Britain for six months.
(b) Calculate how much interest he receives for the six months.
(Total 8 marks)
5. Angela needs $4000 to pay for a car. She was given two options by the car seller.
Option A: Outright Loan
A loan of $4000 at a rate of 12% per annum compounded monthly.
(a) Find
(i) the cost of this loan for one year;
(2)
(ii) the equivalent annual simple interest rate.
(2)
Option B: Friendly Credit Terms
A 25% deposit, followed by 12 equal monthly payments of $287.50.
(b) (i) How much is to be paid as a deposit under this option?
(1)
(ii) Find the cost of the loan under Friendly Credit Terms.
(2)
(c) Give a reason why Angela might choose
(i) Option A
(ii) Option B
(2)(Total 9 marks)
6. Miranti deposits $1000 into an investment account that pays 5% interest per annum.
(a) What will be the value of the investment after 5 years if the interest is reinvested?
(2)
(b) How many years would it take Miranti’s investment of $1000 to double in value?
(4)
At the beginning of each year Brenda deposits $1000 into an investment account that pays 5% interest per annum. Interest is calculated annually and reinvested.
(c) How much would be in Brenda’s account after 5 years?
(4)
(Total 10 marks)
7. The table shows part of a currency conversion chart. For example GBP 1 is equivalent to FFR 8.33.
| |GBP |USD |FFR |
|GBP |1 |p |8.33 |
|USD |0.64 |1 |q |
|FFR |0.12 |0.19 |l |
For all calculations in this question give your answers correct to two decimal places.
(a) Calculate the value of
(i) p;
(ii) q.
(4)
(b) Joe has USD 1500 to exchange at a bank.
(i) Assuming no commission is charged, how much in GBP will Joe receive from the bank?
(2)
(ii) Assuming the bank charges 1.5% commission,
(a) how much in GBP does Joe pay in commission?
(1)
(b) how much in GBP does Joe actually receive for his USD 1500?
(1)
(c) Joe decides to invest GBP 700 of his money in a savings account which pays interest at 5%, compounded annually.
(i) How much interest will the GBP 700 earn after 4 years?
(2)
(ii) For how many years must Joe invest his GBP 700 in order to earn at least GBP 200 in interest?
(2)
(d) After 4 years Joe has a total of GBP 900 in his savings account on an investment at 5% interest compounded annually. How much did he invest? Give your answer to the nearest one GBP.
(2)
(Total 14 marks)
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