Question:
Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
Correct Answer
$7560
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5400 × 5% × 8
= $5400 ×5/100 × 8
= 5400 × 5 × 8/100
= 27000 × 8/100
= 216000/100
= $2160
Thus, Simple Interest = $2160
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 = $5400 + $2160
= $7560
Thus, Amount to be paid = $7560 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 = $5400
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 5% × 8)
= $5400 + ($5400 ×5/100 × 8)
= $5400 + (5400 × 5 × 8/100)
= $5400 + (27000 × 8/100)
= $5400 + (216000/100)
= $5400 + $2160 = $7560
Thus, Amount (A) to be paid = $7560 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5400, the simple interest in 1 year
= 5/100 × 5400
= 5 × 5400/100
= 27000/100 = $270
Thus, simple interest for 1 year = $270
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $270 × 8 = $2160
Thus, Simple Interest (SI) = $2160
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $2160
= $7560
Thus, Amount to be paid = $7560 Answer
Similar Questions
(1) How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.
(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
(6) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(7) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(9) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
(10) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.