Question:
What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
Correct Answer
$3534
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 7%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 2
= $3100 ×7/100 × 2
= 3100 × 7 × 2/100
= 21700 × 2/100
= 43400/100
= $434
Thus, Simple Interest = $434
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 + $434
= $3534
Thus, Amount to be paid = $3534 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) = 7%
And, Time (t) = 2 years
Thus, Amount (A)
= $3100 + ($3100 × 7% × 2)
= $3100 + ($3100 ×7/100 × 2)
= $3100 + (3100 × 7 × 2/100)
= $3100 + (21700 × 2/100)
= $3100 + (43400/100)
= $3100 + $434 = $3534
Thus, Amount (A) to be paid = $3534 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3100, the simple interest in 1 year
= 7/100 × 3100
= 7 × 3100/100
= 21700/100 = $217
Thus, simple interest for 1 year = $217
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $217 × 2 = $434
Thus, Simple Interest (SI) = $434
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $434
= $3534
Thus, Amount to be paid = $3534 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(2) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(5) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(6) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(7) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(10) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.