Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.
Correct Answer
$9095
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 10%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5350 × 10% × 7
= $5350 ×10/100 × 7
= 5350 × 10 × 7/100
= 53500 × 7/100
= 374500/100
= $3745
Thus, Simple Interest = $3745
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 = $5350 + $3745
= $9095
Thus, Amount to be paid = $9095 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 = $5350
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5350 + ($5350 × 10% × 7)
= $5350 + ($5350 ×10/100 × 7)
= $5350 + (5350 × 10 × 7/100)
= $5350 + (53500 × 7/100)
= $5350 + (374500/100)
= $5350 + $3745 = $9095
Thus, Amount (A) to be paid = $9095 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5350, the simple interest in 1 year
= 10/100 × 5350
= 10 × 5350/100
= 53500/100 = $535
Thus, simple interest for 1 year = $535
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $535 × 7 = $3745
Thus, Simple Interest (SI) = $3745
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $3745
= $9095
Thus, Amount to be paid = $9095 Answer
Similar Questions
(1) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.
(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(5) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
(7) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(8) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
(10) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.