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) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(2) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.
(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?
(5) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.
(6) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(8) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(9) If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.