Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
Correct Answer
$9180
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 7%
Time (t) = 10 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% × 10
= $5400 ×7/100 × 10
= 5400 × 7 × 10/100
= 37800 × 10/100
= 378000/100
= $3780
Thus, Simple Interest = $3780
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 + $3780
= $9180
Thus, Amount to be paid = $9180 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) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 7% × 10)
= $5400 + ($5400 ×7/100 × 10)
= $5400 + (5400 × 7 × 10/100)
= $5400 + (37800 × 10/100)
= $5400 + (378000/100)
= $5400 + $3780 = $9180
Thus, Amount (A) to be paid = $9180 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 10 years
= Simple interest for 1 year × 10
= $378 × 10 = $3780
Thus, Simple Interest (SI) = $3780
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3780
= $9180
Thus, Amount to be paid = $9180 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.
(2) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.
(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(9) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(10) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.