Question:
What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?
Correct Answer
$3565
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 3%
Time (t) = 5 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% × 5
= $3100 ×3/100 × 5
= 3100 × 3 × 5/100
= 9300 × 5/100
= 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) = 3%
And, Time (t) = 5 years
Thus, Amount (A)
= $3100 + ($3100 × 3% × 5)
= $3100 + ($3100 ×3/100 × 5)
= $3100 + (3100 × 3 × 5/100)
= $3100 + (9300 × 5/100)
= $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 = 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 5 years
= Simple interest for 1 year × 5
= $93 × 5 = $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) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(4) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 4 years.
(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(8) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(9) If Mark paid $5104 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 after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.