Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 8 years.
Correct Answer
$7548
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5100 ×6/100 × 8
= 5100 × 6 × 8/100
= 30600 × 8/100
= 244800/100
= $2448
Thus, Simple Interest = $2448
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 + $2448
= $7548
Thus, Amount to be paid = $7548 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5100 + ($5100 × 6% × 8)
= $5100 + ($5100 ×6/100 × 8)
= $5100 + (5100 × 6 × 8/100)
= $5100 + (30600 × 8/100)
= $5100 + (244800/100)
= $5100 + $2448 = $7548
Thus, Amount (A) to be paid = $7548 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5100, the simple interest in 1 year
= 6/100 × 5100
= 6 × 5100/100
= 30600/100 = $306
Thus, simple interest for 1 year = $306
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $306 × 8 = $2448
Thus, Simple Interest (SI) = $2448
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2448
= $7548
Thus, Amount to be paid = $7548 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(4) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(5) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.
(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(8) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?