Question:
Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.
Correct Answer
$9180
Solution And Explanation
Solution
Given,
Principal (P) = $5400
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) = $5400 × 10% × 7
= $5400 ×10/100 × 7
= 5400 × 10 × 7/100
= 54000 × 7/100
= 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) = 10%
And, Time (t) = 7 years
Thus, Amount (A)
= $5400 + ($5400 × 10% × 7)
= $5400 + ($5400 ×10/100 × 7)
= $5400 + (5400 × 10 × 7/100)
= $5400 + (54000 × 7/100)
= $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 = 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 7 years
= Simple interest for 1 year × 7
= $540 × 7 = $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) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(2) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?
(4) In how much time a principal of $3000 will amount to $3360 at a simple interest of 3% per annum?
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?
(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(8) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 9% simple interest?
(9) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 6% simple interest?
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.