Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
Correct Answer
$8670
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 10%
Time (t) = 7 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% × 7
= $5100 ×10/100 × 7
= 5100 × 10 × 7/100
= 51000 × 7/100
= 357000/100
= $3570
Thus, Simple Interest = $3570
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 + $3570
= $8670
Thus, Amount to be paid = $8670 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) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 10% × 7)
= $5100 + ($5100 ×10/100 × 7)
= $5100 + (5100 × 10 × 7/100)
= $5100 + (51000 × 7/100)
= $5100 + (357000/100)
= $5100 + $3570 = $8670
Thus, Amount (A) to be paid = $8670 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 7 years
= Simple interest for 1 year × 7
= $510 × 7 = $3570
Thus, Simple Interest (SI) = $3570
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3570
= $8670
Thus, Amount to be paid = $8670 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(3) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?
(6) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.
(8) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?
(9) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(10) How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?