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) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(2) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 2% simple interest?
(4) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(8) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(9) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?