Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
Correct Answer
$8476
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 7%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 9
= $5200 ×7/100 × 9
= 5200 × 7 × 9/100
= 36400 × 9/100
= 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 7% × 9)
= $5200 + ($5200 ×7/100 × 9)
= $5200 + (5200 × 7 × 9/100)
= $5200 + (36400 × 9/100)
= $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 = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5200, the simple interest in 1 year
= 7/100 × 5200
= 7 × 5200/100
= 36400/100 = $364
Thus, simple interest for 1 year = $364
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $364 × 9 = $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) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(5) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?
(9) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(10) 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.