Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.
Correct Answer
$3968
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 7%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 4
= $3100 ×7/100 × 4
= 3100 × 7 × 4/100
= 21700 × 4/100
= 86800/100
= $868
Thus, Simple Interest = $868
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 + $868
= $3968
Thus, Amount to be paid = $3968 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) = 7%
And, Time (t) = 4 years
Thus, Amount (A)
= $3100 + ($3100 × 7% × 4)
= $3100 + ($3100 ×7/100 × 4)
= $3100 + (3100 × 7 × 4/100)
= $3100 + (21700 × 4/100)
= $3100 + (86800/100)
= $3100 + $868 = $3968
Thus, Amount (A) to be paid = $3968 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3100, the simple interest in 1 year
= 7/100 × 3100
= 7 × 3100/100
= 21700/100 = $217
Thus, simple interest for 1 year = $217
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $217 × 4 = $868
Thus, Simple Interest (SI) = $868
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $868
= $3968
Thus, Amount to be paid = $3968 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(2) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(3) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?
(4) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.
(6) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(8) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.