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Math

QuestionHow much should Adam deposit to earn \$100 interest in 4 years at a 5% simple interest rate? A) \$400 B) \$500 C) \$1,500 D) \$2,000

Studdy Solution

STEP 1

Assumptions1. The interest to be earned is $100. The interest rate is5%
3. The time for earning the interest is4 years4. The interest is calculated using simple interest, not compounding5. The principal amount that needs to be deposited is unknown

STEP 2

We need to use the formula for simple interest to find the principal amount. The formula for simple interest isInterest=Principal amounttimesInterest ratetimesTimeInterest = Principal\, amount \\times Interest\, rate \\times Time

STEP 3

We can rearrange the formula to solve for the principal amountPrincipal amount=InterestInterest ratetimesTimePrincipal\, amount = \frac{Interest}{Interest\, rate \\times Time}

STEP 4

Now, plug in the given values for the interest, interest rate, and time to calculate the principal amount.
Principal amount=$100%times4Principal\, amount = \frac{\$100}{\% \\times4}

STEP 5

Convert the percentage to a decimal value.
5%=0.055\% =0.05Principal amount=$1000.05times4Principal\, amount = \frac{\$100}{0.05 \\times4}

STEP 6

Calculate the principal amount.
Principal amount=$1000.05times4=$500Principal\, amount = \frac{\$100}{0.05 \\times4} = \$500Adam needs to deposit 500inthesavingsaccounttoearn500 in the savings account to earn 100 in interest over4 years at a5% simple annual interest rate. The correct answer is B) $500.

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