Question:
Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
Correct Answer
$8493
Solution And Explanation
Solution
Given,
Principal (P) = $5700
Rate of Simple Interest (SI) = 7%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $5700 × 7% × 7
= $5700 ×7/100 × 7
= 5700 × 7 × 7/100
= 39900 × 7/100
= 279300/100
= $2793
Thus, Simple Interest = $2793
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 = $5700 + $2793
= $8493
Thus, Amount to be paid = $8493 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 = $5700
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5700 + ($5700 × 7% × 7)
= $5700 + ($5700 ×7/100 × 7)
= $5700 + (5700 × 7 × 7/100)
= $5700 + (39900 × 7/100)
= $5700 + (279300/100)
= $5700 + $2793 = $8493
Thus, Amount (A) to be paid = $8493 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5700, the simple interest in 1 year
= 7/100 × 5700
= 7 × 5700/100
= 39900/100 = $399
Thus, simple interest for 1 year = $399
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $399 × 7 = $2793
Thus, Simple Interest (SI) = $2793
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5700 + $2793
= $8493
Thus, Amount to be paid = $8493 Answer
Similar Questions
(1) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
(4) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(6) How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
(7) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(9) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.