Question:
Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.
Correct Answer
$5200
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 10%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $4000 × 10% × 3
= $4000 ×10/100 × 3
= 4000 × 10 × 3/100
= 40000 × 3/100
= 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 = $4000 + $1200
= $5200
Thus, Amount to be paid = $5200 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 = $4000
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $4000 + ($4000 × 10% × 3)
= $4000 + ($4000 ×10/100 × 3)
= $4000 + (4000 × 10 × 3/100)
= $4000 + (40000 × 3/100)
= $4000 + (120000/100)
= $4000 + $1200 = $5200
Thus, Amount (A) to be paid = $5200 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $4000, the simple interest in 1 year
= 10/100 × 4000
= 10 × 4000/100
= 40000/100 = $400
Thus, simple interest for 1 year = $400
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $400 × 3 = $1200
Thus, Simple Interest (SI) = $1200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $1200
= $5200
Thus, Amount to be paid = $5200 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(2) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(4) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 4% simple interest?
(5) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(8) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(10) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.