Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 3 years.
Correct Answer
$3379
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 3%
Time (t) = 3 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% × 3
= $3100 ×3/100 × 3
= 3100 × 3 × 3/100
= 9300 × 3/100
= 27900/100
= $279
Thus, Simple Interest = $279
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 + $279
= $3379
Thus, Amount to be paid = $3379 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) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 3% × 3)
= $3100 + ($3100 ×3/100 × 3)
= $3100 + (3100 × 3 × 3/100)
= $3100 + (9300 × 3/100)
= $3100 + (27900/100)
= $3100 + $279 = $3379
Thus, Amount (A) to be paid = $3379 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 3 years
= Simple interest for 1 year × 3
= $93 × 3 = $279
Thus, Simple Interest (SI) = $279
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $279
= $3379
Thus, Amount to be paid = $3379 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.
(2) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(5) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(7) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(9) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.