Question:
Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
Correct Answer
$7290
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 5%
Time (t) = 7 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% × 7
= $5400 ×5/100 × 7
= 5400 × 5 × 7/100
= 27000 × 7/100
= 189000/100
= $1890
Thus, Simple Interest = $1890
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 + $1890
= $7290
Thus, Amount to be paid = $7290 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) = 7 years
Thus, Amount (A)
= $5400 + ($5400 × 5% × 7)
= $5400 + ($5400 ×5/100 × 7)
= $5400 + (5400 × 5 × 7/100)
= $5400 + (27000 × 7/100)
= $5400 + (189000/100)
= $5400 + $1890 = $7290
Thus, Amount (A) to be paid = $7290 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 7 years
= Simple interest for 1 year × 7
= $270 × 7 = $1890
Thus, Simple Interest (SI) = $1890
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1890
= $7290
Thus, Amount to be paid = $7290 Answer
Similar Questions
(1) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
(5) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(8) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?