Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
Correct Answer
$3472
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 4%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $3100 × 4% × 3
= $3100 ×4/100 × 3
= 3100 × 4 × 3/100
= 12400 × 3/100
= 37200/100
= $372
Thus, Simple Interest = $372
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 = $3100 + $372
= $3472
Thus, Amount to be paid = $3472 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 = $3100
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 4% × 3)
= $3100 + ($3100 ×4/100 × 3)
= $3100 + (3100 × 4 × 3/100)
= $3100 + (12400 × 3/100)
= $3100 + (37200/100)
= $3100 + $372 = $3472
Thus, Amount (A) to be paid = $3472 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3100, the simple interest in 1 year
= 4/100 × 3100
= 4 × 3100/100
= 12400/100 = $124
Thus, simple interest for 1 year = $124
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $124 × 3 = $372
Thus, Simple Interest (SI) = $372
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $372
= $3472
Thus, Amount to be paid = $3472 Answer
Similar Questions
(1) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?
(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
(5) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?
(6) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?
(7) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.
(9) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.