Question:
Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
Correct Answer
$10200
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 10%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 10
= $5100 ×10/100 × 10
= 5100 × 10 × 10/100
= 51000 × 10/100
= 510000/100
= $5100
Thus, Simple Interest = $5100
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 + $5100
= $10200
Thus, Amount to be paid = $10200 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) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5100 + ($5100 × 10% × 10)
= $5100 + ($5100 ×10/100 × 10)
= $5100 + (5100 × 10 × 10/100)
= $5100 + (51000 × 10/100)
= $5100 + (510000/100)
= $5100 + $5100 = $10200
Thus, Amount (A) to be paid = $10200 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5100, the simple interest in 1 year
= 10/100 × 5100
= 10 × 5100/100
= 51000/100 = $510
Thus, simple interest for 1 year = $510
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $510 × 10 = $5100
Thus, Simple Interest (SI) = $5100
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $5100
= $10200
Thus, Amount to be paid = $10200 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?
(4) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(5) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.
(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.
(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.