Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
Correct Answer
$3720
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 5%
Time (t) = 4 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% × 4
= $3100 ×5/100 × 4
= 3100 × 5 × 4/100
= 15500 × 4/100
= 62000/100
= $620
Thus, Simple Interest = $620
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 + $620
= $3720
Thus, Amount to be paid = $3720 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) = 4 years
Thus, Amount (A)
= $3100 + ($3100 × 5% × 4)
= $3100 + ($3100 ×5/100 × 4)
= $3100 + (3100 × 5 × 4/100)
= $3100 + (15500 × 4/100)
= $3100 + (62000/100)
= $3100 + $620 = $3720
Thus, Amount (A) to be paid = $3720 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 4 years
= Simple interest for 1 year × 4
= $155 × 4 = $620
Thus, Simple Interest (SI) = $620
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $620
= $3720
Thus, Amount to be paid = $3720 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.
(3) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(4) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 8% simple interest?
(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?
(6) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(9) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.