Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.
Correct Answer
$7155
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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) = $5300 × 5% × 7
= $5300 ×5/100 × 7
= 5300 × 5 × 7/100
= 26500 × 7/100
= 185500/100
= $1855
Thus, Simple Interest = $1855
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 = $5300 + $1855
= $7155
Thus, Amount to be paid = $7155 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 = $5300
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5300 + ($5300 × 5% × 7)
= $5300 + ($5300 ×5/100 × 7)
= $5300 + (5300 × 5 × 7/100)
= $5300 + (26500 × 7/100)
= $5300 + (185500/100)
= $5300 + $1855 = $7155
Thus, Amount (A) to be paid = $7155 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5300, the simple interest in 1 year
= 5/100 × 5300
= 5 × 5300/100
= 26500/100 = $265
Thus, simple interest for 1 year = $265
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $265 × 7 = $1855
Thus, Simple Interest (SI) = $1855
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $1855
= $7155
Thus, Amount to be paid = $7155 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(2) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.
(5) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.
(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.