Question:
Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
Correct Answer
$8736
Solution And Explanation
Solution
Given,
Principal (P) = $5600
Rate of Simple Interest (SI) = 7%
Time (t) = 8 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% × 8
= $5600 ×7/100 × 8
= 5600 × 7 × 8/100
= 39200 × 8/100
= 313600/100
= $3136
Thus, Simple Interest = $3136
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 + $3136
= $8736
Thus, Amount to be paid = $8736 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) = 8 years
Thus, Amount (A)
= $5600 + ($5600 × 7% × 8)
= $5600 + ($5600 ×7/100 × 8)
= $5600 + (5600 × 7 × 8/100)
= $5600 + (39200 × 8/100)
= $5600 + (313600/100)
= $5600 + $3136 = $8736
Thus, Amount (A) to be paid = $8736 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 8 years
= Simple interest for 1 year × 8
= $392 × 8 = $3136
Thus, Simple Interest (SI) = $3136
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $3136
= $8736
Thus, Amount to be paid = $8736 Answer
Similar Questions
(1) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 8 years.
(3) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(6) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?
(8) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(9) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(10) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.