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) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(7) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 8 years.
(9) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?