Question:
Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
Correct Answer
$9880
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5200 ×9/100 × 10
= 5200 × 9 × 10/100
= 46800 × 10/100
= 468000/100
= $4680
Thus, Simple Interest = $4680
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 + $4680
= $9880
Thus, Amount to be paid = $9880 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5200 + ($5200 × 9% × 10)
= $5200 + ($5200 ×9/100 × 10)
= $5200 + (5200 × 9 × 10/100)
= $5200 + (46800 × 10/100)
= $5200 + (468000/100)
= $5200 + $4680 = $9880
Thus, Amount (A) to be paid = $9880 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5200, the simple interest in 1 year
= 9/100 × 5200
= 9 × 5200/100
= 46800/100 = $468
Thus, simple interest for 1 year = $468
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $468 × 10 = $4680
Thus, Simple Interest (SI) = $4680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $4680
= $9880
Thus, Amount to be paid = $9880 Answer
Similar Questions
(1) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 2% simple interest?
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.
(5) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.