Question:
Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.
Correct Answer
$6490
Solution And Explanation
Solution
Given,
Principal (P) = $5500
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $5500 × 2% × 9
= $5500 ×2/100 × 9
= 5500 × 2 × 9/100
= 11000 × 9/100
= 99000/100
= $990
Thus, Simple Interest = $990
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $990
= $6490
Thus, Amount to be paid = $6490 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $5500
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5500 + ($5500 × 2% × 9)
= $5500 + ($5500 ×2/100 × 9)
= $5500 + (5500 × 2 × 9/100)
= $5500 + (11000 × 9/100)
= $5500 + (99000/100)
= $5500 + $990 = $6490
Thus, Amount (A) to be paid = $6490 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5500, the simple interest in 1 year
= 2/100 × 5500
= 2 × 5500/100
= 11000/100 = $110
Thus, simple interest for 1 year = $110
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $110 × 9 = $990
Thus, Simple Interest (SI) = $990
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5500 + $990
= $6490
Thus, Amount to be paid = $6490 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(3) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(4) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(6) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.