Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 7 years.
Correct Answer
$6464
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 4%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 7
= $5050 ×4/100 × 7
= 5050 × 4 × 7/100
= 20200 × 7/100
= 141400/100
= $1414
Thus, Simple Interest = $1414
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 + $1414
= $6464
Thus, Amount to be paid = $6464 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) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 4% × 7)
= $5050 + ($5050 ×4/100 × 7)
= $5050 + (5050 × 4 × 7/100)
= $5050 + (20200 × 7/100)
= $5050 + (141400/100)
= $5050 + $1414 = $6464
Thus, Amount (A) to be paid = $6464 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5050, the simple interest in 1 year
= 4/100 × 5050
= 4 × 5050/100
= 20200/100 = $202
Thus, simple interest for 1 year = $202
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $202 × 7 = $1414
Thus, Simple Interest (SI) = $1414
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $1414
= $6464
Thus, Amount to be paid = $6464 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(2) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(3) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
(4) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 7% simple interest?
(5) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.
(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(8) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.