Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
Correct Answer
$8640
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 6%
Time (t) = 10 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) = $5400 × 6% × 10
= $5400 ×6/100 × 10
= 5400 × 6 × 10/100
= 32400 × 10/100
= 324000/100
= $3240
Thus, Simple Interest = $3240
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 + $3240
= $8640
Thus, Amount to be paid = $8640 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) = 6%
And, Time (t) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 6% × 10)
= $5400 + ($5400 ×6/100 × 10)
= $5400 + (5400 × 6 × 10/100)
= $5400 + (32400 × 10/100)
= $5400 + (324000/100)
= $5400 + $3240 = $8640
Thus, Amount (A) to be paid = $8640 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 $5400, the simple interest in 1 year
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = $324
Thus, simple interest for 1 year = $324
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $324 × 10 = $3240
Thus, Simple Interest (SI) = $3240
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3240
= $8640
Thus, Amount to be paid = $8640 Answer
Similar Questions
(1) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?
(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(3) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(5) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?
(6) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(8) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?
(10) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.