Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.
Correct Answer
$3472
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 3%
Time (t) = 4 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) = $3100 × 3% × 4
= $3100 ×3/100 × 4
= 3100 × 3 × 4/100
= 9300 × 4/100
= 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) = 3%
And, Time (t) = 4 years
Thus, Amount (A)
= $3100 + ($3100 × 3% × 4)
= $3100 + ($3100 ×3/100 × 4)
= $3100 + (3100 × 3 × 4/100)
= $3100 + (9300 × 4/100)
= $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 = 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 $3100, the simple interest in 1 year
= 3/100 × 3100
= 3 × 3100/100
= 9300/100 = $93
Thus, simple interest for 1 year = $93
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $93 × 4 = $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) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(2) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
(3) Thomas had to pay $4370 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(5) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?
(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(7) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?
(8) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.