Compound Interest, SMB-030

Michelle decided to invest some of her money at a higher interest rate. She deposited $3000 in an account paying 8.2% per annum, compounding half yearly.

Write down an expression involving the compound interest formula that can be used to find the value of Michelle’s $3000 investment at the end of two years. Find this value correct to the nearest cent. (2 marks)

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How much interest will the $3000 investment earn over a four-year period?

Write your answer correct to the nearest cent. (2 marks)

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Show Answers Only

`$3523.09`
`$1137.40`

Show Worked Solution

a. `text{Interest rate}\ (r) = \frac{8.2%}{2} = 4.1% = 0.041\ \ \text{(per 6 months)}`

`text(Compounding periods)\ (n) = 2 xx 2 = 4`

`FV`	`= PV(1+r)^n`
	`= 3000(1.041)^4`
	`= 3523.093…`
	`= $3523.09\ \ text{(nearest cent)}`

b. `text{Compounding periods}\ (n) = 4 xx 2 = 8`

`FV`	`= 3000(1.041)^8`
	`= 4137.396…`

`:.\ text(Interest earned)`	`= 4137.40-3000`
	`= $1137.40\ \ text{(nearest cent)}`