Question:
Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
Correct Answer
$9412
Solution And Explanation
Solution
Given,
Principal (P) = $5200
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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% × 9
= $5200 ×9/100 × 9
= 5200 × 9 × 9/100
= 46800 × 9/100
= 421200/100
= $4212
Thus, Simple Interest = $4212
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 + $4212
= $9412
Thus, Amount to be paid = $9412 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) = 9 years
Thus, Amount (A)
= $5200 + ($5200 × 9% × 9)
= $5200 + ($5200 ×9/100 × 9)
= $5200 + (5200 × 9 × 9/100)
= $5200 + (46800 × 9/100)
= $5200 + (421200/100)
= $5200 + $4212 = $9412
Thus, Amount (A) to be paid = $9412 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 9 years
= Simple interest for 1 year × 9
= $468 × 9 = $4212
Thus, Simple Interest (SI) = $4212
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5200 + $4212
= $9412
Thus, Amount to be paid = $9412 Answer
Similar Questions
(1) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?
(4) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?
(8) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(9) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.