Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.
Correct Answer
$5814
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 2%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 7
= $5100 ×2/100 × 7
= 5100 × 2 × 7/100
= 10200 × 7/100
= 71400/100
= $714
Thus, Simple Interest = $714
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 + $714
= $5814
Thus, Amount to be paid = $5814 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) = 2%
And, Time (t) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 2% × 7)
= $5100 + ($5100 ×2/100 × 7)
= $5100 + (5100 × 2 × 7/100)
= $5100 + (10200 × 7/100)
= $5100 + (71400/100)
= $5100 + $714 = $5814
Thus, Amount (A) to be paid = $5814 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5100, the simple interest in 1 year
= 2/100 × 5100
= 2 × 5100/100
= 10200/100 = $102
Thus, simple interest for 1 year = $102
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $102 × 7 = $714
Thus, Simple Interest (SI) = $714
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $714
= $5814
Thus, Amount to be paid = $5814 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(3) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(5) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(7) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?
(8) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(9) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.
(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.