Question:
Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.
Correct Answer
$8476
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 9%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 7
= $5200 ×9/100 × 7
= 5200 × 9 × 7/100
= 46800 × 7/100
= 327600/100
= $3276
Thus, Simple Interest = $3276
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 + $3276
= $8476
Thus, Amount to be paid = $8476 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) = 9%
And, Time (t) = 7 years
Thus, Amount (A)
= $5200 + ($5200 × 9% × 7)
= $5200 + ($5200 ×9/100 × 7)
= $5200 + (5200 × 9 × 7/100)
= $5200 + (46800 × 7/100)
= $5200 + (327600/100)
= $5200 + $3276 = $8476
Thus, Amount (A) to be paid = $8476 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5200, the simple interest in 1 year
= 9/100 × 5200
= 9 × 5200/100
= 46800/100 = $468
Thus, simple interest for 1 year = $468
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $468 × 7 = $3276
Thus, Simple Interest (SI) = $3276
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $3276
= $8476
Thus, Amount to be paid = $8476 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.
(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?
(4) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(5) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(7) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(9) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7084 to clear the loan, then find the time period of the loan.
(10) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.