Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.
Correct Answer
$8344
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $5600 × 7% × 7
= $5600 ×7/100 × 7
= 5600 × 7 × 7/100
= 39200 × 7/100
= 274400/100
= $2744
Thus, Simple Interest = $2744
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 = $5600 + $2744
= $8344
Thus, Amount to be paid = $8344 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 = $5600
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5600 + ($5600 × 7% × 7)
= $5600 + ($5600 ×7/100 × 7)
= $5600 + (5600 × 7 × 7/100)
= $5600 + (39200 × 7/100)
= $5600 + (274400/100)
= $5600 + $2744 = $8344
Thus, Amount (A) to be paid = $8344 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 $5600, the simple interest in 1 year
= 7/100 × 5600
= 7 × 5600/100
= 39200/100 = $392
Thus, simple interest for 1 year = $392
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $392 × 7 = $2744
Thus, Simple Interest (SI) = $2744
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $2744
= $8344
Thus, Amount to be paid = $8344 Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 7% simple interest?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
(3) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(4) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(6) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
(7) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.
(8) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(10) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.