Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
Correct Answer
$7540
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 5%
Time (t) = 9 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) = $5200 × 5% × 9
= $5200 ×5/100 × 9
= 5200 × 5 × 9/100
= 26000 × 9/100
= 234000/100
= $2340
Thus, Simple Interest = $2340
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 + $2340
= $7540
Thus, Amount to be paid = $7540 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 5% × 9)
= $5200 + ($5200 ×5/100 × 9)
= $5200 + (5200 × 5 × 9/100)
= $5200 + (26000 × 9/100)
= $5200 + (234000/100)
= $5200 + $2340 = $7540
Thus, Amount (A) to be paid = $7540 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 $5200, the simple interest in 1 year
= 5/100 × 5200
= 5 × 5200/100
= 26000/100 = $260
Thus, simple interest for 1 year = $260
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $260 × 9 = $2340
Thus, Simple Interest (SI) = $2340
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $2340
= $7540
Thus, Amount to be paid = $7540 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 4 years.
(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(9) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?