Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
Correct Answer
$3596
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 4%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 4
= $3100 ×4/100 × 4
= 3100 × 4 × 4/100
= 12400 × 4/100
= 49600/100
= $496
Thus, Simple Interest = $496
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 + $496
= $3596
Thus, Amount to be paid = $3596 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) = 4%
And, Time (t) = 4 years
Thus, Amount (A)
= $3100 + ($3100 × 4% × 4)
= $3100 + ($3100 ×4/100 × 4)
= $3100 + (3100 × 4 × 4/100)
= $3100 + (12400 × 4/100)
= $3100 + (49600/100)
= $3100 + $496 = $3596
Thus, Amount (A) to be paid = $3596 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3100, the simple interest in 1 year
= 4/100 × 3100
= 4 × 3100/100
= 12400/100 = $124
Thus, simple interest for 1 year = $124
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $124 × 4 = $496
Thus, Simple Interest (SI) = $496
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $496
= $3596
Thus, Amount to be paid = $3596 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(3) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 4% simple interest?
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?
(7) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(9) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.