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) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(2) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.
(3) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(5) Robert had to pay $3472 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 if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(8) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.