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) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.
(4) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(5) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(8) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(10) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.