Question:
Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
Correct Answer
$6448
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5200 ×3/100 × 8
= 5200 × 3 × 8/100
= 15600 × 8/100
= 124800/100
= $1248
Thus, Simple Interest = $1248
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 + $1248
= $6448
Thus, Amount to be paid = $6448 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 3% × 8)
= $5200 + ($5200 ×3/100 × 8)
= $5200 + (5200 × 3 × 8/100)
= $5200 + (15600 × 8/100)
= $5200 + (124800/100)
= $5200 + $1248 = $6448
Thus, Amount (A) to be paid = $6448 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5200, the simple interest in 1 year
= 3/100 × 5200
= 3 × 5200/100
= 15600/100 = $156
Thus, simple interest for 1 year = $156
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $156 × 8 = $1248
Thus, Simple Interest (SI) = $1248
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $1248
= $6448
Thus, Amount to be paid = $6448 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(4) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?
(6) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(9) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.