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) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 2% simple interest for 8 years.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.
(8) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8930 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 10% simple interest.