Question:
Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.
Correct Answer
$7668
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 7
= $5400 ×6/100 × 7
= 5400 × 6 × 7/100
= 32400 × 7/100
= 226800/100
= $2268
Thus, Simple Interest = $2268
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 + $2268
= $7668
Thus, Amount to be paid = $7668 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) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5400 + ($5400 × 6% × 7)
= $5400 + ($5400 ×6/100 × 7)
= $5400 + (5400 × 6 × 7/100)
= $5400 + (32400 × 7/100)
= $5400 + (226800/100)
= $5400 + $2268 = $7668
Thus, Amount (A) to be paid = $7668 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5400, the simple interest in 1 year
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = $324
Thus, simple interest for 1 year = $324
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $324 × 7 = $2268
Thus, Simple Interest (SI) = $2268
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $2268
= $7668
Thus, Amount to be paid = $7668 Answer
Similar Questions
(1) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(2) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.
(5) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(7) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(8) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.