Question:
Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
Correct Answer
$9720
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 10%
Time (t) = 8 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) = $5400 × 10% × 8
= $5400 ×10/100 × 8
= 5400 × 10 × 8/100
= 54000 × 8/100
= 432000/100
= $4320
Thus, Simple Interest = $4320
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 + $4320
= $9720
Thus, Amount to be paid = $9720 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 10% × 8)
= $5400 + ($5400 ×10/100 × 8)
= $5400 + (5400 × 10 × 8/100)
= $5400 + (54000 × 8/100)
= $5400 + (432000/100)
= $5400 + $4320 = $9720
Thus, Amount (A) to be paid = $9720 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 $5400, the simple interest in 1 year
= 10/100 × 5400
= 10 × 5400/100
= 54000/100 = $540
Thus, simple interest for 1 year = $540
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $540 × 8 = $4320
Thus, Simple Interest (SI) = $4320
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $4320
= $9720
Thus, Amount to be paid = $9720 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?
(4) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(5) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(8) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.