Question:
Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
Correct Answer
$7171
Solution And Explanation
Solution
Given,
Principal (P) = $5050
Rate of Simple Interest (SI) = 6%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 7
= $5050 ×6/100 × 7
= 5050 × 6 × 7/100
= 30300 × 7/100
= 212100/100
= $2121
Thus, Simple Interest = $2121
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 + $2121
= $7171
Thus, Amount to be paid = $7171 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) = 6%
And, Time (t) = 7 years
Thus, Amount (A)
= $5050 + ($5050 × 6% × 7)
= $5050 + ($5050 ×6/100 × 7)
= $5050 + (5050 × 6 × 7/100)
= $5050 + (30300 × 7/100)
= $5050 + (212100/100)
= $5050 + $2121 = $7171
Thus, Amount (A) to be paid = $7171 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5050, the simple interest in 1 year
= 6/100 × 5050
= 6 × 5050/100
= 30300/100 = $303
Thus, simple interest for 1 year = $303
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $303 × 7 = $2121
Thus, Simple Interest (SI) = $2121
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5050 + $2121
= $7171
Thus, Amount to be paid = $7171 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.
(3) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(4) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.
(6) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?
(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 3 years.