Question:
Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.
Correct Answer
$6534
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 3%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 7
= $5400 ×3/100 × 7
= 5400 × 3 × 7/100
= 16200 × 7/100
= 113400/100
= $1134
Thus, Simple Interest = $1134
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 + $1134
= $6534
Thus, Amount to be paid = $6534 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) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5400 + ($5400 × 3% × 7)
= $5400 + ($5400 ×3/100 × 7)
= $5400 + (5400 × 3 × 7/100)
= $5400 + (16200 × 7/100)
= $5400 + (113400/100)
= $5400 + $1134 = $6534
Thus, Amount (A) to be paid = $6534 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5400, the simple interest in 1 year
= 3/100 × 5400
= 3 × 5400/100
= 16200/100 = $162
Thus, simple interest for 1 year = $162
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $162 × 7 = $1134
Thus, Simple Interest (SI) = $1134
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1134
= $6534
Thus, Amount to be paid = $6534 Answer
Similar Questions
(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(3) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(5) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?
(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(7) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.