1203AFE Lecture Notes - Lecture 4: Promissory Note, Effective Interest Rate, Interest

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30 May 2018

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Week 4 Money, Bank and Finance

Numeracy 2- Introduction to Financial Maths

Simple Interest

• Simple Interest is interest that is charged only on the principal or the amount of

money borrowed.

• Simple interest is calculated using the formula:

o I is the simple interest amount

o P is the principal or the amount borrowed or invested

o r is the (annual) rate of interest

o t is the time period of the loan or investment, which may be in whole

numbers (for a number of years) or stated as a fraction of 365 days for some

part of one year

Example

• Find the simple interest on a loan of $20,000 for three years at an annual rate of 12%

• Solving for P

o John knows that in 6 months he will have to pay tuition fees at college of

$365. He wants to deposit a sum of money now and use the interest on the

principal to pay the fees in 6 months time. He can earn an annual rate of 12%

on his money. How much should he invest now to earn the fees?

PV and FV

• The future value (FV) of a sum of money is the principal plus interest, or the amount

received in the future.

• The present value (PV) is the sum invested or borrowed today, or the principal. It is

also the future value discounted back to today using the applicable interest rate and

number of time periods.

• Time value of money - Clearly if someone offers

you $1,000 you would prefer to receive the money

now rather than in one years time.

Example- Time Value of Money

• For example, the present value of $1,000 to be

received in one years tie is alulated as (at

10%):

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Example- Future Value

• FV formula is derived from the simple interest formula as for a single sum is defined

as:

• Loan for $40,000, annual simple interest rate is 12%, repaid in 9 months.

• What is the FV (i.e. how much is to be repaid including interest in 9 months?)

Example- Present Value

• The present value of a sum of money is its value today. We can rearrange the

formula for the future value of a single sum to:

• Amount invested at time zero (now) to give a

future value of $600 in 45 days at 7% interest?

Simple Discount

• For some securities a simple discount applies.

• The interest charge is based on the maturity value of the security and the borrower

receives less than the full amount borrowed.

• The discount (D) is calculated as the future value (FV) multiplied by the discount rate

(d) multiplied by the number of years (t).

• The present value, or price, then becomes

the future value less the discount.

Example

• A loan for $3000, 2 years, simple discount rate

of 9%.

• Calculate interest on the loan. →

• Interest = $540 and the proceeds of the loan

are therefore $3,000 less the discount of $540, which equals $2,460.

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Document Summary

Simple interest: simple interest is interest that is charged only on the principal or the amount of money borrowed, simple interest is calculated using the formula: Example: find the simple interest on a loan of ,000 for three years at an annual rate of 12, solving for p, john knows that in 6 months he will have to pay tuition fees at college of. He wants to deposit a sum of money now and use the interest on the principal to pay the fees in 6 months time. He can earn an annual rate of 12% on his money. Pv and fv: the future value (fv) of a sum of money is the principal plus interest, or the amount received in the future, the present value (pv) is the sum invested or borrowed today, or the principal. Example- time value of money: for example, the present value of ,000 to be received in one year(cid:859)s ti(cid:373)e is (cid:272)al(cid:272)ulated as (at.

Related Questions

it is about Simple Interest Future Value

1-Logan borrowed $3,300 from his friend at 4% simple interest. He plans to repay the loan at the end of 1 month. If the principal and interest are repaid in one lump sum, how much money must he give his friend to retire the loan?

2-Jason deposited $1,500 into an account earning 3.6% simple interest. How much money will the account be worth at the end of 6 months?

3-Rasheed won $5,050 at a casino. He deposited his winnings into an account earning 4% interest. How much will the account be worth at the end of 9 months?

4-Linda deposited $1,000 into an account paying 4% simple interest. At the end of 3 months, how much money will she have?

5- Dana deposited $30,000 into an account paying 3.6% simple interest. After 6 months, how much money will she have?

6-Nicholas deposited $50,000 into an account earning 2% simple interest, how much money will be in the account at the end of 7 months?

7-Suppose $50,000 is deposited into an account that pays 4% simple interest. How much money will be in the account at the end of 6 months?

8-Oscar made $3,000 during the summer. He deposited all his summer earnings into an account earning 4% simple interest. How much money will he have in 11 months?

9-An account earns 3% simple interest. If $7,000 was deposited today, what will the account be worth at the end of 8 months?

10-Sherry deposited $1,001 into an account paying 5% simple interest, how much money will she have in the account at the end of 3 months?

chocolateraven243

Case 1. Car

John can afford to spend $500 per month on a car. He figures he needs half of it for gas, parking, and insurance. He has been to the bank, and they will loan him 100% of the car's purchase price.

a) If his loan is at a nominal 12% annual rate over 36 months, what is the most expensive car he can purchase?

b) The car he likes costs $14,000 and the dealer will finance it over 60 months at 12%. Can he afford it? If not, for how many months will he need to save his $500 per month?

c) What is the highest interest rate he can pay over 60 months and stay within his budget if he buys the $14,000 car now?

Case 2. Mortgage

a) Assume mortgage payments of $1000 per month for 30 years and an interest rate of 0.5% per month. What initial principal or PW will this repay?

b) Assume annual mortgage payments of $12,000 for 30 years and an interest rate of 6% per year. What initial principal or PW will this repay?

c) Assume annual mortgage payments of $12,000 for 30 years and an interest rate of 6.168% per year. What initial principal or PW will this repay?

Graphs: For each case (car/mortgage) at least one graph, which you can use to back up your discussion. For example, plot the interest payment + principal payment + balance.

question 1:Hazel needs $7000 for her first year tuition at Lake head University when she graduates in 2 years. She plans to make deposits into an account that earns 6.5% per year, compounded bi-weekly. How much should she deposit bi-weekly to meet her target amount.

question2: Edosa borrowed some money at 9.6%/a compounded monthly. Two years later, he paid $2000 toward the principal and the interest. After another, year, he paid another $2000. After another three years, he paid the remainder of the principal and the interest, which totaled $3000. How much money did he original borrow?

question 3: Bernard opens a savings account and invested $3196.88. How many years would Bernard need to keep his money in the savings account if the interest rate is 5.75%/a, compounded semi-annually, if he wants to make $5000?

question4: Filmon is putting his summer earnings into an annuity from which he can draw living expenses while he is at university. He will need to withdraw $900 per month for 8 months. Interest is earned at a rate of 6% compounded monthly. How much does Filmon need to invest at the beginning of the school year to finance the annuity.

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1203AFE Lecture Notes - Lecture 4: Promissory Note, Effective Interest Rate, Interest

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