Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
Correct Answer
$8008
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5200 × 6% × 9
= $5200 ×6/100 × 9
= 5200 × 6 × 9/100
= 31200 × 9/100
= 280800/100
= $2808
Thus, Simple Interest = $2808
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 = $5200 + $2808
= $8008
Thus, Amount to be paid = $8008 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 = $5200
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 6% × 9)
= $5200 + ($5200 ×6/100 × 9)
= $5200 + (5200 × 6 × 9/100)
= $5200 + (31200 × 9/100)
= $5200 + (280800/100)
= $5200 + $2808 = $8008
Thus, Amount (A) to be paid = $8008 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5200, the simple interest in 1 year
= 6/100 × 5200
= 6 × 5200/100
= 31200/100 = $312
Thus, simple interest for 1 year = $312
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $312 × 9 = $2808
Thus, Simple Interest (SI) = $2808
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2808
= $8008
Thus, Amount to be paid = $8008 Answer
Similar Questions
(1) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(2) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(3) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(7) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(8) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(9) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.