Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
Correct Answer
$7673.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
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) = $5150 × 7% × 7
= $5150 ×7/100 × 7
= 5150 × 7 × 7/100
= 36050 × 7/100
= 252350/100
= $2523.5
Thus, Simple Interest = $2523.5
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 = $5150 + $2523.5
= $7673.5
Thus, Amount to be paid = $7673.5 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 = $5150
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 7% × 7)
= $5150 + ($5150 ×7/100 × 7)
= $5150 + (5150 × 7 × 7/100)
= $5150 + (36050 × 7/100)
= $5150 + (252350/100)
= $5150 + $2523.5 = $7673.5
Thus, Amount (A) to be paid = $7673.5 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 $5150, the simple interest in 1 year
= 7/100 × 5150
= 7 × 5150/100
= 36050/100 = $360.5
Thus, simple interest for 1 year = $360.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $360.5 × 7 = $2523.5
Thus, Simple Interest (SI) = $2523.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2523.5
= $7673.5
Thus, Amount to be paid = $7673.5 Answer
Similar Questions
(1) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?
(2) William had to pay $3710 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 Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
(6) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(8) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(10) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.