smc-604-10-Simple interest

Recursion and Finance, GEN1 2024 VCAA 20 MC

Dainika invested $2000 for three years at 4.4% per annum, compounding quarterly.

To earn the same amount of interest in three years in a simple interest account, the annual simple interest rate would need to be closest to

4.60%
4.68%
4.84%
4.98%

Show Answers Only

$B$

Show Worked Solution

$FV$	$=2000\left(1-\dfrac{0.044}{4}\right)^{12}$
	$=$2280.57$
$\text{Interest pa}$	$=\dfrac{280.57}{3}=$93.52$

$\text{SI rate}$	$=\dfrac{93.52}{2000}\times 100\%$
	$=4.676\dots\%$

$\Rightarrow B$

CORE*, FUR2 2006 VCAA 3

The company prepares for this expenditure by establishing three different investments.

$7000 is invested at a simple interest rate of 6.25% per annum for eight years.

Determine the total value of this investment at the end of eight years. (2 marks)
$10 000 is invested at an interest rate of 6% per annum compounding quarterly for eight years.

Determine the total value of this investment at the end of eight years.

Write your answer correct to the nearest dollar. (1 mark)
$500 is deposited into an account with an interest rate of 6.5% per annum compounding monthly.

Deposits of $200 are made to this account on the last day of each month after interest has been paid.

Determine the total value of this investment at the end of eight years.

Write your answer correct to the nearest dollar. (1 mark)

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`$10\ 500`
`$16\ 103`
`$25\ 935`

Show Worked Solution

a.	`I`	`= (PrT)/100`
		`= (7000 xx 6.25 xx 8)/100`
		`= $3500`

`:.\ text(Total value of investment)`

`= 7000 + 3500`

`= $10\ 500`

b. `text(Compounding periods) = 8 xx 4 = 32`

`text(Interest rate)`	`= (text(6%))/4`
	`= 1.5text(% per quarter)`

`:.\ text(Total value of investment)`

`= PR^n`

`= 10\ 000(1.015)^32`

`= 16\ 103.24…`

`= $16\ 103\ \ text{(nearest $)}`

c. `text(By TVM Solver,)`

`N`	`= 8 xx 12 = 96`
`I(text(%))`	`= 6.5`
`PV`	`= 500`
`PMT`	`= 200`
`FV`	`= ?`
`text(P/Y)`	`= text(C/Y) = 12`

`=> FV = −25\ 935.30…`

`:.\ text(Total value of investment is $25 935.)`

CORE*, FUR2 2008 VCAA 1

Michelle has a bank account that pays her simple interest.

The bank statement below shows the transactions on Michelle’s account for the month of July.

What amount, in dollars, was deposited in cash on 11 July? (1 mark)

Interest for this account is calculated on the minimum monthly balance at a rate of 3% per annum.

Calculate the interest for July, correct to the nearest cent. (2 marks)

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`$620`
`$15.30`

Show Worked Solution

a.	`text(Deposit)`	`= 6870.67-6250.67`
		`= $620`

b. `text(Minimum Balance) = $6120.86`

`:.\ text(Interest)`	`=(PrT)/100`
	`= 6120.86 xx 3/100 xx 1/12`
	`= 15.302…`
	`= $15.30`

CORE*, FUR2 2010 VCAA 3

Simple Saver is a simple interest investment in which interest is paid annually.

Growth Plus is a compound interest investment in which interest is paid annually.

Initially, $8000 is invested with both Simple Saver and Growth Plus.

The graph below shows the total value (principal and all interest earned) of each of these investments over a 15 year period.

The increase in the value of each investment over time is due to interest

Which investment pays the highest annual interest rate, Growth Plus or Simple Saver?

Give a reason to justify your answer. (1 mark)
After 15 years, the total value (principal and all interest earned) of the Simple Saver investment is $21 800.

Find the amount of interest paid annually. (1 mark)
After 15 years, the total value (principal and all interest earned) of the Growth Plus investment is $24 000.
1. Write down an equation that can be used to ﬁnd the annual compound interest rate, `r`. (1 mark)
2. Determine the annual compound interest rate.
  
  Write your answer as a percentage correct to one decimal place. (1 mark)

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`text(Simple Saver has the highest annual)`
`text(interest rate because after 1 year,)`
`text(the value of investment is higher.)`
`$920`
1. `24\ 000 = 8000 (1 + r/100)^15`
2. `7.6text{% (1 d.p.)}`

Show Worked Solution

a. `text(Simple Saver has the highest annual)`

♦♦♦ Part (a) was “very” poorly answered although exact data unavailable.
MARKER’S COMMENT: Most students ignored the word “rate” and instead referred to the eventual return of each investment.

`text(interest rate because after 1 year,)`

`text(the value of investment is higher.)`

b. `text(Total interest earned)`

`= 21\ 800 – 8000`

`= $13\ 800`

`:.\ text(Interest paid annually)`

`= (13\ 800)/15`

`= $920`

c.i. `text(Using)\ A = PR^n,`

`24\ 000 = 8000 (1 + r/100)^15`

c.ii.	`(1 + r/100)^15`	`= 3`
	`1 + r/100`	`= 1.0759…`
	`:. r`	`= 0.0759…`
		`= 7.6text{% (1 d.p.)}`

CORE*, FUR1 2015 VCAA 6 MC

The transaction details for a savings account for the month of August 2014 are shown in the table below.

The table is incomplete.

Interest is calculated and paid monthly on the minimum balance for that month.

The annual rate of interest paid on this account is closest to

A. `text(3.10%)`

B. `text(3.11%)`

C. `text(3.57%)`

D. `text(3.75%)`

E. `text(14.9%)`

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`D`

Show Worked Solution

`text(Minimum balance) = $4870.50`

♦ Mean mark 46%.

`text(Interest)`	`= 5885.72-5870.50`
	`= $15.22`

`15.22`	`=PrT`
`15.22`	`= 4870.50 xx r xx 1/12`
`:. r`	`=(12 xx 15.22)/4870.50`
	`= 3.74…text(%)`

`=> D`

CORE*, FUR1 2010 VCAA 2 MC

$6000 is invested in an account that earns simple interest at the rate of 3.5% per annum.

The total interest earned in the first four years is

A. `$70`

B. `$84`

C. `$210`

D. `$840`

E. `$885`

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`D`

Show Worked Solution

`P = 6000,\ \ r = 3.5,\ \ T = 4`

`I`	`= (PrT) / 100`
`I`	`= {(6000) (3.5) (4)} / 100`
	`= 840`

`=> D`

CORE*, FUR2 2014 VCAA 1

The adult membership fee for a cricket club is $150.

Junior members are offered a discount of $30 off the adult membership fee.

Write down the discount for junior members as a percentage of the adult membership fee. (1 mark)

Adult members of the cricket club pay $15 per match in addition to the membership fee of $150.

If an adult member played 12 matches, what is the total this member would pay to the cricket club? (1 mark)

If a member does not pay the membership fee by the due date, the club will charge simple interest at the rate of 5% per month until the fee is paid.

Michael paid the $150 membership fee exactly two months after the due date.

Calculate, in dollars, the interest that Michael will be charged. (1 mark)

The cricket club received a statement of the transactions in its savings account for the month of January 2014.

The statement is shown below.

1. Calculate the amount of the withdrawal on 17 January 2014. (1 mark)
2. Interest for this account is calculated on the minimum balance for the month and added to the account on the last day of the month.
  
  What is the annual rate of interest for this account?
  
  Write your answer, correct to one decimal place. (1 mark)

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`text(20%)`
`$330`
`$15`
1. `$17\ 000`
2. `3.5`

Show Worked Solution

a. `text(Discount for junior members)`

`= 30/150 xx 100text(%)`

`= 20text(%)`

b.	`text(Match Payments)`	`= 12 xx 15=$180`

`:.\ text(Total paid to the club)`

`= 150 + 180`

`= $330`

c.	`I`	`= (PrT)/100`
		`= (150 xx 5 xx 2)/100`
		`= $15`

d.i. `text(Withdrawal on 17-Jan)`

`= 59\ 700 – 42\ 700`

`= $17\ 000`

d.ii. `text(Minimum Jan balance) = $42\ 700`

`47\ 200 xx r xx 1/12`	`= 125.12`
`:. r`	`= (125.12 xx 12)/(42\ 700)`
	`= 0.0351…`

`:.\ text(Annual interest rate) = 3.5text(%)`

CORE*, FUR1 2009 VCAA 1 MC

An amount of $800 is invested for two years at a simple interest rate of 4% per annum.

The total amount of interest earned by the investment is

A. $32

B. $64

C. $160

D. $320

E. $640

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`B`

Show Worked Solution

`I`	`= (PrT)/100`
	`= ((800)(4)(2))/100`
	`= $64`

`=> B`

CORE*, FUR1 2008 VCAA 6 MC

Sam and Charlie each invest $5000 for three years.

Sam’s investment earns simple interest at the rate of 7.5% per annum.

Charlie’s investment earns interest at the rate of 7.5% per annum compounding annually.

At the conclusion of three years, correct to the nearest cent, Sam will have

A. $86.48 less than Charlie.

B. $86.48 more than Charlie.

C. $132.23 less than Charlie.

D. $132.23 more than Charlie.

E. the same as Charlie.

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`A`

Show Worked Solution

`text(Sam’s Investment,)`

`I`	`= (PrT)/100`
	`= ((5000)(7.5)(3))/100`
	`= 1125`

`:.\ text(Total amount)`	`= 5000 + 1125`
	`= $6125`

`text(Charlie’s Investment,)`

`A`	`= PR^n`
	`= (5000)(1.075)^3`
	`= $6211.48`

`text(Difference)`	`= 6211.48-6125`
	`= $86.48`

`=> A`

CORE*, FUR1 2007 VCAA 3 MC

A sum of money is invested in an account paying simple interest at a rate of 8% per annum.

The total interest earned on this investment over 6 years is $27 000.

The sum of money invested is

`$12\ 960`
`$45\ 000`
`$56\ 250`
`$202\ 500`
`$337\ 500`

Show Answers Only

`C`

Show Worked Solution

`I = 27 \ 000, \ \ r = 8/100, \ \ T = 6`

`I`	`= (PrT)/100`
`27 \ 000`	`= (P xx 8 xx 6)/100`
`P`	`= (2\ 700\ 000)/48`
	`= 56\ 250`

`=> C`

CORE*, FUR1 2006 VCAA 1 MC

$4000 is invested at a simple interest rate of 5% per annum.

The amount of interest earned in the first year is

A. `$20`

B. `$200`

C. `$220`

D. `$420`

E. `$2000`

Show Answers Only

`B`

Show Worked Solution

`I`	`= (PrT)/100`
	`= (4000 xx 5 xx 1)/100`
	`= $200`

`=> B`

CORE*, FUR1 2012 VCAA 2 MC

$3000 is invested at a simple interest rate of 6.5% per annum.

The total interest earned in three years is

A. `$195.00`

B. `$580.50`

C. `$585.00`

D. `$3623.85`

E. `$3585.00`

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`C`

Show Worked Solution

`P = 3000,\ \ r = 6.5,\ \ T = 3`

`text(Using)\ \ I`	`=(PrT)/100`
`:. I`	`= (3000 xx 6.5 xx 3) / 100`
	`= $585`

`=> C`

CORE*, FUR1 2013 VCAA 7 MC

The graph below shows the growth in value of a $1000 investment over a period of four years.

A different amount of money is invested under the same investment conditions for eight years.

In total, the amount of interest earned on this investment is $600.

The amount of money invested is

A. `$500`

B. `$600`

C. `$1500`

D. `$2000`

E. `$2400`

Show Answers Only

`C`

Show Worked Solution

`text(From the graph)`

`text(Flat rate) = 50 / 1000 xx 100text(%)=5text(% p.a.)`

`text(Using)\ \ \ I = (PrT) / 100,\ \ \ text(where)`

`I = 600,\ \ r = 5,\ \ T = 8`

`600`	`= (P xx 5 xx 8) / 100`
`:.P`	`= (600 xx 100) / (5 xx 8)`
	`= 1500`

`=> C`

\(FV\)	\(=2000\left(1-\dfrac{0.044}{4}\right)^{12}\)
	\(=$2280.57\)
\(\text{Interest pa}\)	\(=\dfrac{280.57}{3}=$93.52\)

\(\text{SI rate}\)	\(=\dfrac{93.52}{2000}\times 100\%\)
	\(=4.676\dots\%\)