Question:
Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.
Correct Answer
$8528
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $5200 × 8% × 8
= $5200 ×8/100 × 8
= 5200 × 8 × 8/100
= 41600 × 8/100
= 332800/100
= $3328
Thus, Simple Interest = $3328
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 = $5200 + $3328
= $8528
Thus, Amount to be paid = $8528 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 = $5200
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5200 + ($5200 × 8% × 8)
= $5200 + ($5200 ×8/100 × 8)
= $5200 + (5200 × 8 × 8/100)
= $5200 + (41600 × 8/100)
= $5200 + (332800/100)
= $5200 + $3328 = $8528
Thus, Amount (A) to be paid = $8528 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5200, the simple interest in 1 year
= 8/100 × 5200
= 8 × 5200/100
= 41600/100 = $416
Thus, simple interest for 1 year = $416
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $416 × 8 = $3328
Thus, Simple Interest (SI) = $3328
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $3328
= $8528
Thus, Amount to be paid = $8528 Answer
Similar Questions
(1) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(2) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(4) How much loan did Jason borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9240 to clear it?
(5) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(7) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.
(9) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(10) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.