Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
Correct Answer
$9880
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5200 ×10/100 × 9
= 5200 × 10 × 9/100
= 52000 × 9/100
= 468000/100
= $4680
Thus, Simple Interest = $4680
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 + $4680
= $9880
Thus, Amount to be paid = $9880 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 10% × 9)
= $5200 + ($5200 ×10/100 × 9)
= $5200 + (5200 × 10 × 9/100)
= $5200 + (52000 × 9/100)
= $5200 + (468000/100)
= $5200 + $4680 = $9880
Thus, Amount (A) to be paid = $9880 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5200, the simple interest in 1 year
= 10/100 × 5200
= 10 × 5200/100
= 52000/100 = $520
Thus, simple interest for 1 year = $520
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $520 × 9 = $4680
Thus, Simple Interest (SI) = $4680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $4680
= $9880
Thus, Amount to be paid = $9880 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(3) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 8 years.
(9) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
(10) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?