Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.
Correct Answer
$10800
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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) = $5400 × 10% × 10
= $5400 ×10/100 × 10
= 5400 × 10 × 10/100
= 54000 × 10/100
= 540000/100
= $5400
Thus, Simple Interest = $5400
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 + $5400
= $10800
Thus, Amount to be paid = $10800 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) = 10%
And, Time (t) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 10% × 10)
= $5400 + ($5400 ×10/100 × 10)
= $5400 + (5400 × 10 × 10/100)
= $5400 + (54000 × 10/100)
= $5400 + (540000/100)
= $5400 + $5400 = $10800
Thus, Amount (A) to be paid = $10800 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 $5400, the simple interest in 1 year
= 10/100 × 5400
= 10 × 5400/100
= 54000/100 = $540
Thus, simple interest for 1 year = $540
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $540 × 10 = $5400
Thus, Simple Interest (SI) = $5400
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $5400
= $10800
Thus, Amount to be paid = $10800 Answer
Similar Questions
(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.
(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?
(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(4) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 7 years.
(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.