Question:
Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.
Correct Answer
$6750
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5000 × 5% × 7
= $5000 ×5/100 × 7
= 5000 × 5 × 7/100
= 25000 × 7/100
= 175000/100
= $1750
Thus, Simple Interest = $1750
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 = $5000 + $1750
= $6750
Thus, Amount to be paid = $6750 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 = $5000
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5000 + ($5000 × 5% × 7)
= $5000 + ($5000 ×5/100 × 7)
= $5000 + (5000 × 5 × 7/100)
= $5000 + (25000 × 7/100)
= $5000 + (175000/100)
= $5000 + $1750 = $6750
Thus, Amount (A) to be paid = $6750 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5000, the simple interest in 1 year
= 5/100 × 5000
= 5 × 5000/100
= 25000/100 = $250
Thus, simple interest for 1 year = $250
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $250 × 7 = $1750
Thus, Simple Interest (SI) = $1750
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $1750
= $6750
Thus, Amount to be paid = $6750 Answer
Similar Questions
(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(3) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(8) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(10) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.