Question:
Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.
Correct Answer
$8528
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5200 ×8/100 × 8
= 5200 × 8 × 8/100
= 41600 × 8/100
= 332800/100
= $3328
Thus, Simple Interest = $3328
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 + $3328
= $8528
Thus, Amount to be paid = $8528 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 8% × 8)
= $5200 + ($5200 ×8/100 × 8)
= $5200 + (5200 × 8 × 8/100)
= $5200 + (41600 × 8/100)
= $5200 + (332800/100)
= $5200 + $3328 = $8528
Thus, Amount (A) to be paid = $8528 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5200, the simple interest in 1 year
= 8/100 × 5200
= 8 × 5200/100
= 41600/100 = $416
Thus, simple interest for 1 year = $416
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $416 × 8 = $3328
Thus, Simple Interest (SI) = $3328
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $3328
= $8528
Thus, Amount to be paid = $8528 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(2) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(3) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.
(4) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(5) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(8) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(9) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(10) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.