Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.
Correct Answer
$6528
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 4%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 7
= $5100 ×4/100 × 7
= 5100 × 4 × 7/100
= 20400 × 7/100
= 142800/100
= $1428
Thus, Simple Interest = $1428
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 + $1428
= $6528
Thus, Amount to be paid = $6528 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) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 4% × 7)
= $5100 + ($5100 ×4/100 × 7)
= $5100 + (5100 × 4 × 7/100)
= $5100 + (20400 × 7/100)
= $5100 + (142800/100)
= $5100 + $1428 = $6528
Thus, Amount (A) to be paid = $6528 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5100, the simple interest in 1 year
= 4/100 × 5100
= 4 × 5100/100
= 20400/100 = $204
Thus, simple interest for 1 year = $204
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $204 × 7 = $1428
Thus, Simple Interest (SI) = $1428
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1428
= $6528
Thus, Amount to be paid = $6528 Answer
Similar Questions
(1) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 4% simple interest?
(2) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
(4) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(5) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.
(7) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?
(9) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?