Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
Correct Answer
$8493
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5700 × 7% × 7
= $5700 ×7/100 × 7
= 5700 × 7 × 7/100
= 39900 × 7/100
= 279300/100
= $2793
Thus, Simple Interest = $2793
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 = $5700 + $2793
= $8493
Thus, Amount to be paid = $8493 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 = $5700
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 7% × 7)
= $5700 + ($5700 ×7/100 × 7)
= $5700 + (5700 × 7 × 7/100)
= $5700 + (39900 × 7/100)
= $5700 + (279300/100)
= $5700 + $2793 = $8493
Thus, Amount (A) to be paid = $8493 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5700, the simple interest in 1 year
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = $399
Thus, simple interest for 1 year = $399
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $399 × 7 = $2793
Thus, Simple Interest (SI) = $2793
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2793
= $8493
Thus, Amount to be paid = $8493 Answer
Similar Questions
(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(2) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(3) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(4) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9536 to clear the loan, then find the time period of the loan.
(5) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(6) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(9) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(10) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.