Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
Correct Answer
$4216
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 9%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 4
= $3100 ×9/100 × 4
= 3100 × 9 × 4/100
= 27900 × 4/100
= 111600/100
= $1116
Thus, Simple Interest = $1116
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 + $1116
= $4216
Thus, Amount to be paid = $4216 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) = 9%
And, Time (t) = 4 years
Thus, Amount (A)
= $3100 + ($3100 × 9% × 4)
= $3100 + ($3100 ×9/100 × 4)
= $3100 + (3100 × 9 × 4/100)
= $3100 + (27900 × 4/100)
= $3100 + (111600/100)
= $3100 + $1116 = $4216
Thus, Amount (A) to be paid = $4216 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3100, the simple interest in 1 year
= 9/100 × 3100
= 9 × 3100/100
= 27900/100 = $279
Thus, simple interest for 1 year = $279
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $279 × 4 = $1116
Thus, Simple Interest (SI) = $1116
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1116
= $4216
Thus, Amount to be paid = $4216 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(2) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(6) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.
(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) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.