Interest: Simple Interest
Derrick deposited $700 in a savings account that pays 2.5% simple __quarterly__ interest. After the initial deposit, he did not make any deposits or withdrawals. How many years ago did he invest the money if his current balance on the account is $980?
Incorrect.
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Incorrect.
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Incorrect.
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__Alternative Method__:
Given that Derrick deposited $700 and his current balance is $980, he earned $280 in interest. The number of years for which the amount was deposited can be calculated as follows:
>$$\text{Simple interest} = \text{Principal} \times \text{Interest rate} \times \text{Time}$$
>$$\$280 = \$700 \times 0.025 \times \text{Time}$$
>$$280 = 7\times 2.5\times \text{Time}$$
Then solve for Time.
>$$\displaystyle \text{Time} = \frac{280}{7 \times 2.5}$$
>>$$\displaystyle = \frac{40}{2.5}$$
>>$$\displaystyle = \frac{400}{25}$$
>>$$\displaystyle = 16$$.
Given that 2.5% interest is earned on a quarterly basis, time here is calculated in quarters. In order to calculate the number of years, divide the number of quarters by 4.
>$$\displaystyle \frac{16}{4} = 4 \text{ years}$$.
Incorrect.
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Did you forget to divide by 4? Read the question carefully—2.5% interest is earned on a quarterly basis (not annually).
Correct.
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Since Derrick deposited $700 and his current balance is $980, he earned $280 in interest.
>$$\displaystyle \text{Percentage interest earned} = \frac{\$280}{\$700} \times 100 = \frac{280 }{ 7} = 40\%$$
Since quarterly interest earned is 2.5% and this percentage is fixed for simple interest, the amount was deposited for
>$$\displaystyle \frac{40\%}{ 2.5\%} = \frac{80}{5} = 16 \text{ quarters}$$.
Divide by 4 to convert this to years:
>$$\displaystyle \frac{16}{4} = 4 \text{ years}$$.
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