Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
Correct Answer
$3565
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 5%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 3
= $3100 ×5/100 × 3
= 3100 × 5 × 3/100
= 15500 × 3/100
= 46500/100
= $465
Thus, Simple Interest = $465
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 + $465
= $3565
Thus, Amount to be paid = $3565 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) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 5% × 3)
= $3100 + ($3100 ×5/100 × 3)
= $3100 + (3100 × 5 × 3/100)
= $3100 + (15500 × 3/100)
= $3100 + (46500/100)
= $3100 + $465 = $3565
Thus, Amount (A) to be paid = $3565 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3100, the simple interest in 1 year
= 5/100 × 3100
= 5 × 3100/100
= 15500/100 = $155
Thus, simple interest for 1 year = $155
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $155 × 3 = $465
Thus, Simple Interest (SI) = $465
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $465
= $3565
Thus, Amount to be paid = $3565 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.
(3) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(4) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(7) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(8) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?
(9) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.