Question:
Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.
Correct Answer
$8791
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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) = $5900 × 7% × 7
= $5900 ×7/100 × 7
= 5900 × 7 × 7/100
= 41300 × 7/100
= 289100/100
= $2891
Thus, Simple Interest = $2891
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 = $5900 + $2891
= $8791
Thus, Amount to be paid = $8791 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 = $5900
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5900 + ($5900 × 7% × 7)
= $5900 + ($5900 ×7/100 × 7)
= $5900 + (5900 × 7 × 7/100)
= $5900 + (41300 × 7/100)
= $5900 + (289100/100)
= $5900 + $2891 = $8791
Thus, Amount (A) to be paid = $8791 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 $5900, the simple interest in 1 year
= 7/100 × 5900
= 7 × 5900/100
= 41300/100 = $413
Thus, simple interest for 1 year = $413
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $413 × 7 = $2891
Thus, Simple Interest (SI) = $2891
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $2891
= $8791
Thus, Amount to be paid = $8791 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(2) 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.
(3) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?
(4) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 4% simple interest?
(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(7) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(10) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?