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) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.
(2) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(4) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?
(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(7) How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(10) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.