Question:
Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
Correct Answer
$8046
Solution And Explanation
Solution
Given,
Principal (P) = $5400
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) = $5400 × 7% × 7
= $5400 ×7/100 × 7
= 5400 × 7 × 7/100
= 37800 × 7/100
= 264600/100
= $2646
Thus, Simple Interest = $2646
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 = $5400 + $2646
= $8046
Thus, Amount to be paid = $8046 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 = $5400
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5400 + ($5400 × 7% × 7)
= $5400 + ($5400 ×7/100 × 7)
= $5400 + (5400 × 7 × 7/100)
= $5400 + (37800 × 7/100)
= $5400 + (264600/100)
= $5400 + $2646 = $8046
Thus, Amount (A) to be paid = $8046 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 $5400, the simple interest in 1 year
= 7/100 × 5400
= 7 × 5400/100
= 37800/100 = $378
Thus, simple interest for 1 year = $378
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $378 × 7 = $2646
Thus, Simple Interest (SI) = $2646
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $2646
= $8046
Thus, Amount to be paid = $8046 Answer
Similar Questions
(1) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.
(3) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(4) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(7) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.