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) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(2) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?
(4) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(6) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?
(8) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(9) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?
(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?