Question:
What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
Correct Answer
$3658
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 9%
Time (t) = 2 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) = $3100 × 9% × 2
= $3100 ×9/100 × 2
= 3100 × 9 × 2/100
= 27900 × 2/100
= 55800/100
= $558
Thus, Simple Interest = $558
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 = $3100 + $558
= $3658
Thus, Amount to be paid = $3658 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 = $3100
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 2 years
Thus, Amount (A)
= $3100 + ($3100 × 9% × 2)
= $3100 + ($3100 ×9/100 × 2)
= $3100 + (3100 × 9 × 2/100)
= $3100 + (27900 × 2/100)
= $3100 + (55800/100)
= $3100 + $558 = $3658
Thus, Amount (A) to be paid = $3658 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 $3100, the simple interest in 1 year
= 9/100 × 3100
= 9 × 3100/100
= 27900/100 = $279
Thus, simple interest for 1 year = $279
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $279 × 2 = $558
Thus, Simple Interest (SI) = $558
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $558
= $3658
Thus, Amount to be paid = $3658 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(3) Elizabeth had to pay $3967.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(6) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(7) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(10) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.