Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
Correct Answer
$9360
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 8%
Time (t) = 10 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% × 10
= $5200 ×8/100 × 10
= 5200 × 8 × 10/100
= 41600 × 10/100
= 416000/100
= $4160
Thus, Simple Interest = $4160
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 + $4160
= $9360
Thus, Amount to be paid = $9360 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) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 8% × 10)
= $5200 + ($5200 ×8/100 × 10)
= $5200 + (5200 × 8 × 10/100)
= $5200 + (41600 × 10/100)
= $5200 + (416000/100)
= $5200 + $4160 = $9360
Thus, Amount (A) to be paid = $9360 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 10 years
= Simple interest for 1 year × 10
= $416 × 10 = $4160
Thus, Simple Interest (SI) = $4160
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $4160
= $9360
Thus, Amount to be paid = $9360 Answer
Similar Questions
(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 8 years.
(2) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(4) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(7) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.
(8) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.