Question:
Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
Correct Answer
$8160
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 6%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5100 × 6% × 10
= $5100 ×6/100 × 10
= 5100 × 6 × 10/100
= 30600 × 10/100
= 306000/100
= $3060
Thus, Simple Interest = $3060
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 = $5100 + $3060
= $8160
Thus, Amount to be paid = $8160 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 = $5100
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5100 + ($5100 × 6% × 10)
= $5100 + ($5100 ×6/100 × 10)
= $5100 + (5100 × 6 × 10/100)
= $5100 + (30600 × 10/100)
= $5100 + (306000/100)
= $5100 + $3060 = $8160
Thus, Amount (A) to be paid = $8160 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5100, the simple interest in 1 year
= 6/100 × 5100
= 6 × 5100/100
= 30600/100 = $306
Thus, simple interest for 1 year = $306
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $306 × 10 = $3060
Thus, Simple Interest (SI) = $3060
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3060
= $8160
Thus, Amount to be paid = $8160 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.
(3) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(5) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(6) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(7) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(8) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(9) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.