Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.
Correct Answer
$7524.5
Solution And Explanation
Solution
Given,
Principal (P) = $5050
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) = $5050 × 7% × 7
= $5050 ×7/100 × 7
= 5050 × 7 × 7/100
= 35350 × 7/100
= 247450/100
= $2474.5
Thus, Simple Interest = $2474.5
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 = $5050 + $2474.5
= $7524.5
Thus, Amount to be paid = $7524.5 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 = $5050
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 7% × 7)
= $5050 + ($5050 ×7/100 × 7)
= $5050 + (5050 × 7 × 7/100)
= $5050 + (35350 × 7/100)
= $5050 + (247450/100)
= $5050 + $2474.5 = $7524.5
Thus, Amount (A) to be paid = $7524.5 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 $5050, the simple interest in 1 year
= 7/100 × 5050
= 7 × 5050/100
= 35350/100 = $353.5
Thus, simple interest for 1 year = $353.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $353.5 × 7 = $2474.5
Thus, Simple Interest (SI) = $2474.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2474.5
= $7524.5
Thus, Amount to be paid = $7524.5 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 8% simple interest?
(3) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
(5) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(7) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?
(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.