Question:
Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.
Correct Answer
$6200
Solution And Explanation
Solution
Given,
Principal (P) = $5000
Rate of Simple Interest (SI) = 3%
Time (t) = 8 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) = $5000 × 3% × 8
= $5000 ×3/100 × 8
= 5000 × 3 × 8/100
= 15000 × 8/100
= 120000/100
= $1200
Thus, Simple Interest = $1200
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 + $1200
= $6200
Thus, Amount to be paid = $6200 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5000 + ($5000 × 3% × 8)
= $5000 + ($5000 ×3/100 × 8)
= $5000 + (5000 × 3 × 8/100)
= $5000 + (15000 × 8/100)
= $5000 + (120000/100)
= $5000 + $1200 = $6200
Thus, Amount (A) to be paid = $6200 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 $5000, the simple interest in 1 year
= 3/100 × 5000
= 3 × 5000/100
= 15000/100 = $150
Thus, simple interest for 1 year = $150
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $150 × 8 = $1200
Thus, Simple Interest (SI) = $1200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $1200
= $6200
Thus, Amount to be paid = $6200 Answer
Similar Questions
(1) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.
(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(6) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(7) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.