Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.
Correct Answer
$3937
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 9%
Time (t) = 3 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% × 3
= $3100 ×9/100 × 3
= 3100 × 9 × 3/100
= 27900 × 3/100
= 83700/100
= $837
Thus, Simple Interest = $837
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 + $837
= $3937
Thus, Amount to be paid = $3937 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) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 9% × 3)
= $3100 + ($3100 ×9/100 × 3)
= $3100 + (3100 × 9 × 3/100)
= $3100 + (27900 × 3/100)
= $3100 + (83700/100)
= $3100 + $837 = $3937
Thus, Amount (A) to be paid = $3937 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 3 years
= Simple interest for 1 year × 3
= $279 × 3 = $837
Thus, Simple Interest (SI) = $837
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $837
= $3937
Thus, Amount to be paid = $3937 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.
(2) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(3) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.
(5) 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.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?
(7) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(8) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.