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) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(2) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(4) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(6) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?