Question 13 A.Sharif deposits $2,500 into a savings account which earns 5% simple interest per year. How much interest will Sharif earn after 2 years? If there are no deposits and no withdrawals, how much will be in the savings account after 12 years? B.Chang put $1000 in an account. The account earns $100 in simple interest in 4 years. What is the annual interest rate? If there are no deposits and no withdrawals, how much will be in the savings account after 15 years? C. A bank offers three savings accounts at the given interest rates. Principal Simple Interest Rate < $500 1.5% $500 – $5,000 2.0 % >$5,000 3.0 % The simple interest rate is determined by the principal. How long does it take an account with a principal of $800 to earn $100 in interest? D.You borrow some money to buy a laptop. The simple interest rate is 15%. You pay off the loan after 5 years. The amount you paid off is $1050. How much did you borrow for the laptop? How much interest did you pay? E.Find the annual interest rate, R, if I = $24, P = $400, and t = 2 years.

Answer 1

Let's break down each question step by step.

A. Sharif's Savings Account

1. Simple Interest Calculation:

   • Principal (P) = $2,500
   • Rate (R) = 5% = 0.05
   • Time (t) = 2 years
   • Simple Interest (I) = P × R × t

   \[ I = 2500 \times 0.05 \times 2 = 2500 \times 0.1 = 250 \]

   After 2 years, Sharif earns $250 in interest.

2. Total Amount After 12 Years:

   • Time (t) = 12 years
   • Total Interest = P × R × t

   \[ I = 2500 \times 0.05 \times 12 = 2500 \times 0.6 = 1500 \]

   Total amount in the savings account: \[ \text{Total Amount} = P + I = 2500 + 1500 = 4000 \]

   After 12 years, the total amount will be $4,000.

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B. Chang's Account

1. Annual Interest Rate Calculation:

   • Simple Interest (I) = $100
   • Principal (P) = $1,000
   • Time (t) = 4 years

   \[ R = \frac{I}{P \times t} = \frac{100}{1000 \times 4} = \frac{100}{4000} = 0.025 \text{ or } 2.5% \]

   The annual interest rate is 2.5%.

2. Total Amount After 15 Years:

   • Total interest after 15 years: \[ I = P \times R \times t = 1000 \times 0.025 \times 15 = 1000 \times 0.375 = 375 \]
   • Total amount: \[ \text{Total Amount} = P + I = 1000 + 375 = 1375 \]

   After 15 years, the total amount will be $1,375.

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C. Time Required for an $800 Principal to Earn $100

1. Using Simple Interest Formula:

   • Principal (P) = $800
   • Interest (I) = $100
   • Rate (R) = 2%

   Rearranging the formula for time (t): \[ t = \frac{I}{P \times R} = \frac{100}{800 \times 0.02} = \frac{100}{16} = 6.25 \text{ years} \]

   It will take 6.25 years for the account to earn $100 in interest.

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D. Amount Borrowed for the Laptop

1. Simple Interest Calculation:

   • Total Amount Paid = $1,050
   • Interest Rate (R) = 15% = 0.15
   • Time (t) = 5 years

   Let the borrowed amount (Principal, P) be \( x \).

   The simple interest paid (I) is: \[ I = P \times R \times t = x \times 0.15 \times 5 = 0.75x \]

   Since total amount paid is Principal + Interest: \[ 1050 = x + 0.75x = 1.75x \] \[ x = \frac{1050}{1.75} = 600 \]

   Amount borrowed for the laptop is $600.

2. Total Interest Paid: \[ I = 0.75 \times 600 = 450 \]

   Total interest paid is $450.

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E. Finding the Annual Interest Rate R

1. Given:

   • Interest (I) = $24
   • Principal (P) = $400
   • Time (t) = 2 years

   Using the formula to find the annual rate (R): \[ R = \frac{I}{P \times t} = \frac{24}{400 \times 2} = \frac{24}{800} = 0.03 \text{ or } 3% \]

   The annual interest rate \( R \) is 3%.