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 after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(2) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(5) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?
(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.
(7) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(8) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.
(10) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?